http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=A22ravi&feedformat=atomstatwiki - User contributions [US]2022-10-03T04:14:41ZUser contributionsMediaWiki 1.28.3http://wiki.math.uwaterloo.ca/statwiki/index.php?title=DCN_plus:_Mixed_Objective_And_Deep_Residual_Coattention_for_Question_Answering&diff=42324DCN plus: Mixed Objective And Deep Residual Coattention for Question Answering2018-12-07T13:11:03Z<p>A22ravi: /* Overview of previous work */ Attention models intuition references added</p>
<hr />
<div>== Introduction ==<br />
Question Answering(QA) is one of the challenging computer science tasks that need an understanding of the natural language and the ability to reason efficiently. To accurately answer the question, the model must first have a detailed understanding of the context the question is being asked from. Because the questions are usually very detailed, having a shallow knowledge from the context would lead to poor and unacceptable performance. Moreover, the model should gather all the information provided in the question and match them with its knowledge from the context. Generating the answer is another interesting task. Based on the dataset the model is meant for, the output of the model might be in a completely different form.<br />
In the past years, QA datasets have improved significantly. Previous datasets were really simple and they usually did not simulate a real-world question-answer pair. For example, Children's book test was one of the popular datasets that have been used for QA for a long time. But the real task for this dataset was to just fill empty spaces in given sentences with the appropriate words. During the past years, the importance of the QA tasks and their practical uses encouraged many to gather and crowdsource useful and more realistic datasets. The Stanford Question Answering Dataset(SQuAD), Microsoft Machine Reading Comprehension Dataset(MS MARCO), and Visual Question Answering Dataset(VQA) are only a few examples of the currently advanced datasets.<br />
As a result of these advancements, many researchers are focusing to improve the performance of the question answering models on these datasets. Deep neural networks were able to outperform the human accuracy on a few of these datasets, but in many cases, there is still a gap between the state-of-the-art and human performance. Previously, Dynamic Coattention Networks(DCN) proved to be efficient on the SQuAD, achieving state-of-the-art performance at the time. In this work, a further modification to DCN has been done which improves the accuracy of the model by proposing a mixed objective that combines cross entropy loss with self-critical policy learning. Moreover, the rewards used are based on the word overlap to find a solution for the evaluation metric and objective misalignment.<br />
<br />
==Overview of previous work==<br />
Most of the current QA models are made from different modules and usually stacked on top of each other. Improving one of the modules would lead to an overall performance of the model. Thus, to evaluate the efficiency of an improvement, researchers usually take a previously submitted model and replace their own improved module with the current one in the model. This is mostly because QA is an interesting discipline and has practical uses.<br />
<br />
The state of the art approaches to this problem can be divided into 3. <br />
<br />
1. Neural Models for question answering: Models like coattention, bidirectional attention flow and self-matching attention build codependent representations of the question and the document. After building these representations, the models predict the answer by generating the start position and the end position corresponding to the estimated answer span. The generation process utilizes a pointer network. Another approach uses a dynamic decoder that iteratively proposes answers by alternating between start position and end position estimates, which in some cases allows it to recover from initial mistakes in predictions. <br />
<br />
2. Neural Attention Models: Models like self-attention have been applied to language modelling and sentimental analysis. A deep version of the same called deep self-attention networks attained state-of-the-art results in machine translation. For an intuitive understanding of attention based neural network models refer the following links: [https://youtu.be/SysgYptB198 Attention Models Intuition 1] [https://youtu.be/quoGRI-1l0A Attention Models Intuition 2]. Coattention, bidirectional attention and self-matching attention are some of the methods that build codependent representation between the question and the document. <br />
<br />
3. Reinforcement learning in NLP: Hierarchical RL techniques have been proposed for generating text in a simulated way finding domain. DQN have been used to learn policies in text-based games using game rewards as feedback. Neural conversational model have been proposed, that is trained using policy gradient methods, whose reward function consisted of heuristics for ease of answering, information flow, and semantic coherence. General actor-critic temporal-difference methods for sequence prediction have also been experimented, performing metric optimization on language modelling and machine translation. Direct word overlap metric optimization have also been applied to summarization and machine translation.<br />
<br />
==Important Terms==<br />
<br />
#Embedding layer: This layer maps each word (or images in the case of visual QA) to a vector space. There are many options to choose for the embedding layer. While pre-trained GloVes or Word2Vecs showed promising results on many tasks, most models use a combination of GloVe and character level embeddings. The character level embeddings are especially useful when dealing with out-of-vocab words. In the case of dealing with images, the embeddings are usually generated using pre-trained ResNets. Using different embedding layers for images has shown to change the overall performance of the model drastically.<br />
#Contextual_layer: The purpose of this layer is to add more features to each word embedding based on the surrounding words and the context. This layer is not presented in many models including the DCN.<br />
#Attention layer: There has been a lot of investigation on the attention mechanisms in recent years. These works, mostly inspired by Bahdanau et al. (2014), try to either modify the basic matrix-based attention mechanism or to develop innovative ones. The sole purpose of the attention mechanism is to make the model able to understand a context, based on the information gathered from somewhere else. For example, in image-based QA, attention layer helps the model to understand the question based on the information provided in the image such as object classes. This way, the model can realize what parts of the question are more important. This model uses '''co-attention layers''' (Xiong, 2017). Given two inputs sources (text and question), internal representations are built conditioned on one of the sources. In a way, this can be thought of as retaining (attending to) parts of the input that are relevant to the other source. From the text, only parts that are 'useful' to the question are kept, while from the question, parts that are useful for the text are retained. The intuition stems from the fact that it is easier to answer a question from a text, knowing the question beforehand compared with when the question is only available at the end. In the former, only information relevant to the question is kept, while in the latter case, all information from the text needs to be kept.<br />
#Output layer: This is the final layer of all models, generating the answer of the question based on the information provided from all the previous layers.<br />
<br />
==DCN+ structure==<br />
The DCN+ is an improvement on the previous DCN model. The overall structure of the model is the same as before. The first improvement is on the coattention module. By introducing a deep residual coattention encoder, the output of the attention layer becomes more feature-rich. The second improvement is achieved by mixing the previous cross-entropy loss with reinforcement learning rewards from self-critical policy learning. DCN+ has a decoder module that is only applicable to the SQuAD dataset since the decoder only predicts an answer span from the given context.<br />
<br />
===Deep residual coattention encoder===<br />
The previous coattention module was unable to grasp complex information based on the context and the question. Recent studies showed that stacked attention mechanisms are outperforming the single layer attention modules. In DCN+, the coattention module is stacked to make it able to self-attend to the context and grasp more information. The second modification is to use residual connectors when merging the coattention output from each layer.<br />
<br />
[[File:Coattention.png|700px|centre]]<br />
<br />
let <math>L^D \in R^{m×d}</math> and <math>L^Q \in R^{n×d}</math> denote the word embedding for the context and the question respectively. Here, <math>d, m, n</math> are the embedding vector size, document word count, and question word count respectively. The model uses a bidirectional LSTM as the contextual layer with shared wights. Also, an additional sentinel token is added at the end of the document and question to make it possible for the model to distinguish between the document and question. <math>E^D</math> and <math>E^Q</math> are outputs of the encoder(contextual) layer.<br />
<br />
\begin{align}<br />
E_1^D = BiLSTM_1(L^D) \in R^{(h×(m+1))}<br />
\end{align}<br />
\begin{align}<br />
E_1^Q = tanh(W BiLSTM_1(L^Q) \in R^{(h×(n+1))}<br />
\end{align}<br />
<br />
Here <math>h</math> is the hidden size of the LSTM. The affinity matrix is created based on the output of the encoder. The affinity matrix is the matrix that the has been used in the attention module from the introduction of attention. By performing a column-wise softmax function on the affinity matrix a vector would be generated that is a representation of the importance of each question token, based on the model's understanding of the context. Similarly, if a row-wise softmax function is applied to the affinity matrix, the output vector would represent the importance of each context word, based on the question. By multiplying these vectors to the outputs of the encoder layer, question-aware context and context-aware question representations would be created.<br />
<br />
\begin{align}<br />
A = {(E_1^D)}^T E_1^Q \in R^{(m+1)×(n+1)}<br />
\end{align}<br />
\begin{align}<br />
{S_1^D} = E_1^Q softmax(A^T) \in R^{h×(m+1)}<br />
\end{align}<br />
\begin{align}<br />
{S_1^Q} = E_1^D softmax(A) \in R^{h×(n+1)}<br />
\end{align}<br />
<br />
To make the question-aware context representation even deeper and more feature-rich, an output (called the co-attention context, <math> C_1^D </math>) of the first co-attention layer is fed directly into the decoder using a residual connection. <br />
<br />
\begin{align}<br />
{C_1^D} = S_1^Q softmax(A^T) \in R^{h×m}<br />
\end{align}<br />
<br />
Note that the model drops the dimension corresponding to the sentinel vector. The summaries also get encoded after this stage, using two bidirectional LSTMs with shared variables.<br />
<br />
\begin{align}<br />
{E_2^D} = BiLSTM_2(S_1^Q) \in R^{2h×m}<br />
\end{align}<br />
\begin{align}<br />
{E_2^Q} = BiLSTM_2(S_1^D) \in R^{2h×n}<br />
\end{align}<br />
<br />
Finally, The <math>E_2^D</math> and <math>E_2^Q</math> are fed into the second co-attention layer. Similar to the first co-attention layer, three outputs are produced, <math>S_2^D, S_2^Q, C_2^D </math>. However, <math>S_2^Q</math> is not used. These co-attention modules can easily get stacked to create a deeper attention mechanism. <br />
<br />
The output of the second co-attention layer are concatenated with residual connections from <math>C_1^D, S_1^D, E_2^D</math>. The final output of model is obtained by passing the concatenated representation through another bi-direction LSTM:<br />
<br />
\begin{align}<br />
U = BiLSTM(concat(E_1^D;E_2^D;S_1^D;S_2^D;C_1^D;C_2^D) \in R^{2h×m}<br />
\end{align}<br />
<br />
===Mixed objective using self-critical policy learning===<br />
DCN produces a distribution over that start and end positions of the answer span. Because of the dynamic nature of the decoder module, it estimates separate distributions over the start and end position of the answer dynamically.<br />
<br />
\begin{align}<br />
l_{ce}(\theta) = - \sum_{t} (log \ p_t^{start}(s|s_{t-1},e_{t-1};\theta) + log \ p_t^{end}(e|s_{t-1},e_{t-1};\theta))<br />
\end{align}<br />
<br />
In the above equation, <math>s</math> and <math>e</math> denote the respective start and end points of the ground truth answer. <math>s_t</math> and <math>e_t</math> denote the greedy estimation of the start and end positions at the <math>t</math>th decoding time step. Similarly, <math>p_t^{start} \in R^m</math> and <math>p_t^{end} \in R^m</math> denote the distribution of the start and end positions respectively. The problem with the above loss functions is that it does not consider the F1 metric for evaluation of the model. There are two metrics to estimate QA models accuracy. The first metric is the exact match and it is a binary score. If the answer string does not match with the ground truth answer even by a single character, the exact match score would be zero. The second metric is the F1 score. F1 score is basically the degree of the overlap between the predicted answer and the ground truth. <br />
For example, suppose there are more than two correct answer spans in a context, <math>A</math> and <math>B</math>, but none of the match the ground truth positions. If A has an exact string match but B does not, The cross-entropy loss would penalize both of them equally. However, if we include can F1 scores in our calculations, the loss function would penalize B and not A. <br />
<br />
The main problem with including F1 score directly into cost functions is that it is non-differentiable. A trick from (Sutton et al.,1999; Schulman et al., 2015) is used to approximate the expected gradient. <br />
For this, DCN+ uses a self-critical reinforcement learning objective.<br />
<br />
\begin{align}<br />
l_{rl}(\theta) = -E_{\hat{\tau} \sim p_\tau} [R(s,e,\hat{s}_T,\hat{e}_T;\theta)]<br />
\end{align}<br />
<br />
\begin{align}<br />
\approx -E_{\hat{\tau} \sim p_\tau} [F_1 (ans(\hat{s}_T, \hat{e}_T), ans(s, e)) - F_1(ans(s_T, e_T), ans(s, e))]<br />
\end{align}<br />
<br />
Here <math>\hat{s} \sim p_t^{start}</math> and <math>\hat{e} \sim p_t^{end}</math> denote the sampled start and end positions respectively from the estimated distributions at <math>t</math>th decoding step. <math>\hat{\tau}</math> is the sequence of sampled start and end positions during all <math>T</math> decoder steps, <math>R</math> is the expected reward, <math>F_1</math> is the F1 score between the predicted answer and the expected answer. Rather than using the raw F1 score, mean subtracted F1 score is used (baseline). Previous studies show that using a baseline for the reward reduces the variance of gradient estimates and facilitates convergence. DCN+ uses a self-critic that uses the F1 produced during greedy inference by the current model.<br />
<br />
[[File:loss.png|700px|centre]]<br />
<br />
==Dataset==<br />
The dataset SQuAD (Reference: Stanford NP Group) was used in training the network. The SQuAD 1.1 dataset contains 100 000 questions, based on a set of Wikipedia articles. These questions are designed to be answered by a segment of text from the article. The solutions to each question are represented by a start location, and the text of the answer. An example question-answer pair of the SQuAD 2.0 dataset is: Q: "When did Beyonce start becoming popular?", A: (text: "in the late 1990s", start: 269).<br />
<br />
The SQuAD 2.0 dataset augments the SQuAD 1.1 collection with 50 000 unanswerable questions, designed in an adversarial manner. Samples were generated by crowdworkers in both cases.<br />
<br />
==Experiments==<br />
To achieve optimal performance, the hyperparameters and training environment are fine-tuned. The hyperparameters of DCN are duplicated. The model was trained and evaluated using the Stanford Question Answering Dataset (SQuAD). For tokenizing the documents, the Stanford CoreNLP reversible tokenizers has been used. For word embeddings, a pre-trained GloVE (trained on 840B common crawl), as well as character ngram embeddings by Hashimoto et al. (2017), is used. Furthermore, these embeddings are then concatenated with context vectors (CoVe) trained on WMT. Words which are not found in the vocabulary have their embedding and context vectors set to zero. The optimizer has been set to Adam and a dropout is also applied on word embeddings that zeros a word embedding with a probability of 0.075. PyTorch is used to build the model.<br />
<br />
==Results==<br />
At the time of submission, the model was able to achieve state-of-the-art results on the SQuAD, outperforming the second model on the leaderboard by 2.0% both on the exact match and F1 scores. It is worth mentioning that a 5% improvement was also achieved with respect to the original DCN model.<br />
<br />
[[File:dcn_resutls1.png|700px|centre]]<br />
<br />
In general, DCN+ was able to a achieve consistent performance improvement in almost every question category.<br />
<br />
[[File:dcn_results2.png|700px|centre]]<br />
<br />
The training curves for DCN+ with reinforcement learning and DCN+ without reinforcement learning are shown in Figure 4 to illustrate the effectiveness of our proposed mixed objective. <br />
<br />
[[File:dcn+.png|700px|centre]]<br />
<br />
===Ablation Study===<br />
An analysis of the significance of each part of the model found that the deep residual coattention contributed the most to the overall performance. The second highest contributor was the mixed objective. The sparse mixture of experts layer in the decoder also provided some minor contributions to improving the overall performance.<br />
<br />
==Summary and Critiques==<br />
<br />
This paper introduces a novel model for the task of question answering where the cross-entropy loss commonly used for such problems previously has been combined with self-critical policy learning. The rewards are obtained from word overlap to solve misalignment metric and optimization objective. This paper improves the state of the art in a popular question-answer data set. The critical drawback in this paper is that it only shows experimental improvements on one question answer dataset. Previous works in the same field have considered performances on at least three different comprehensive question answer data sets. This paper is only an incremental improvement over the previous algorithm DCN which was released a year back. For the policy learning objective, the authors consider the task as a multi-task learning problem where the dual losses are linearly combined. The authors should have used a weighted combination instead as the positional match objective using cross entropy is far more important than the word overlap objective with ground truth. Additionally, some methods adopted by the authors are not intuitive and not much explanation is given for the same. For example, it is not very clear why the F1 scores have been used as RL rewards as against some other distance objectives commonly used in previous works in the same field like cross entropy. The authors mention a common problem in using Reinforcement learning in NLP problems. NLP domains are discontinuous and discrete domains which the agents have to repeatedly explore to find a good policy. RL is very data hungry, but NLP domains don't offer sufficient datasets for exploration in most cases. The paper says that it is treating the optimization problem as a multi-task learning problem to get around the exploration problem. It is not clear how this is effected. <br />
<br />
==Other Sources==<br />
# An easy to understand blog on the base DCN model can be found at [https://einstein.ai/research/blog/state-of-the-art-deep-learning-model-for-question-answering].<br />
# Tensorflow Source code for this model can be found at [https://github.com/andrejonasson/dynamic-coattention-network-plus]<br />
<br />
<br />
<br />
==References==<br />
Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly<br />
learning to align and translate. In ICLR, 2015.<br />
<br />
Dzmitry Bahdanau, Philemon Brakel, Kelvin Xu, Anirudh Goyal, Ryan Lowe, Joelle Pineau,<br />
Aaron C. Courville, and Yoshua Bengio. An actor-critic algorithm for sequence prediction. In<br />
ICLR, 2017.<br />
<br />
Danqi Chen, Adam Fisch, Jason Weston, and Antoine Bordes. Reading Wikipedia to answer open-domain<br />
questions. In ACL, 2017.<br />
<br />
Nina Dethlefs and Heriberto Cuayahuitl. Combining hierarchical reinforcement learning and ´<br />
bayesian networks for natural language generation in situated dialogue. In Proceedings of the<br />
13th European Workshop on Natural Language Generation, pp. 110–120. Association for Computational<br />
Linguistics, 2011.<br />
<br />
Evan Greensmith, Peter L. Bartlett, and Jonathan Baxter. Variance reduction techniques for gradient<br />
estimates in reinforcement learning. Journal of Machine Learning Research, 5:1471–1530, 2001.<br />
<br />
Kazuma Hashimoto, Caiming Xiong, Yoshimasa Tsuruoka, and Richard Socher. A joint many-task<br />
model: Growing a neural network for multiple NLP tasks. In EMNLP, 2017.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition.<br />
2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–<br />
778, 2016.<br />
<br />
Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural computation, 9 8:<br />
1735–80, 1997.<br />
<br />
Alex Kendall, Yarin Gal, and Roberto Cipolla. Multi-task learning using uncertainty to weigh losses<br />
for scene geometry and semantics. CoRR, abs/1705.07115, 2017.<br />
Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. CoRR,<br />
abs/1412.6980, 2014.<br />
<br />
Vijay R. Konda and John N. Tsitsiklis. Actor-critic algorithms. In NIPS, 1999.<br />
Jiwei Li, Will Monroe, Alan Ritter, Michel Galley, Jianfeng Gao, and Dan Jurafsky. Deep reinforcement<br />
learning for dialogue generation. In EMNLP, 2016.<br />
<br />
Rui Liu, Junjie Hu, Wei Wei, Zi Yang, and Eric Nyberg. Structural embedding of syntactic trees for<br />
machine comprehension. In ACL, 2017.<br />
<br />
Jiasen Lu, Jianwei Yang, Dhruv Batra, and Devi Parikh. Hierarchical question-image co-attention<br />
for visual question answering. In NIPS, 2016.<br />
<br />
Christopher D. Manning, Mihai Surdeanu, John Bauer, Jenny Rose Finkel, Steven Bethard, and David McClosky. The stanford corenlp natural language processing toolkit. In ACL, 2014.<br />
<br />
Bryan McCann, James Bradbury, Caiming Xiong, and Richard Socher. Learned in translation: Contextualized word vectors. In NIPS, 2017.<br />
<br />
Microsoft Asia Natural Language Computing Group. R-net: Machine reading comprehension with self-matching networks. 2017.<br />
<br />
Karthik Narasimhan, Tejas D. Kulkarni, and Regina Barzilay. Language understanding for textbased games using deep reinforcement learning. In EMNLP, 2015.<br />
<br />
Romain Paulus, Caiming Xiong, and Richard Socher. A deep reinforced model for abstractive summarization. CoRR, abs/1705.04304, 2017.<br />
<br />
Jeffrey Pennington, Richard Socher, and Christopher D. Manning. Glove: Global vectors for word representation. In EMNLP, 2014.<br />
<br />
Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: 100, 000+ questions for machine comprehension of text. In EMNLP, 2016.<br />
<br />
John Schulman, Nicolas Heess, Theophane Weber, and Pieter Abbeel. Gradient estimation using stochastic computation graphs. In NIPS, 2015.<br />
<br />
Min Joon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. In ICLR, 2017.<br />
<br />
Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, and Jeff Dean. Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. In ICLR, 2017.<br />
<br />
Yelong Shen, Po-Sen Huang, Jianfeng Gao, and Weizhu Chen. Reasonet: Learning to stop reading in machine comprehension. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1047–1055. ACM, 2017.<br />
<br />
Richard S. Sutton, David A. McAllester, Satinder P. Singh, and Yishay Mansour. Policy gradient methods for reinforcement learning with function approximation. In NIPS, 1999.<br />
<br />
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In NIPS, 2017. <br />
<br />
Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In NIPS, 2015.<br />
<br />
Shuohang Wang and Jing Jiang. Machine comprehension using match-lstm and answer pointer. In ICLR, 2017.<br />
<br />
Dirk Weissenborn, Georg Wiese, and Laura Seiffe. Making neural qa as simple as possible but not simpler. In CoNLL, 2017.<br />
<br />
Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V Le, Mohammad Norouzi, Wolfgang Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, et al. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv preprint arXiv:1609.08144, 2016.<br />
<br />
Caiming Xiong, Victor Zhong, and Richard Socher. Dynamic coattention networks for question<br />
answering. In ICLR, 2017.<br />
<br />
Stanford NLP Group. Squad 2.0: The Stanford Question Answering Dataset. https://rajpurkar.github.io/SQuAD-explorer/. Accessed October 24, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DeepVO_Towards_end_to_end_visual_odometry_with_deep_RNN&diff=42289DeepVO Towards end to end visual odometry with deep RNN2018-12-06T12:23:14Z<p>A22ravi: /* Training and Optimization */</p>
<hr />
<div>== Introduction ==<br />
Visual Odometry (VO) is a computer vision technique for estimating an object’s position and orientation from camera images. It is an important technique commonly used for “pose estimation and robot localization” with notable applications in Mars Exploration Rovers and Autonomous Vehicles [x1] [x2]. While the research field of VO is broad, this paper focuses on the topic of monocular visual odometry. Particularly, the authors examine prominent VO methods and argue that mainstream geometry based monocular VO methods should be amended with deep learning approaches. Deep Learning (DL) has recently achieved promising results in computer vision tasks but does not include the VO field, thus the paper proposes a novel deep-learning based end-to-end VO algorithm and then empirically demonstrates its viability.<br />
<br />
== Related Work ==<br />
<br />
Visual odometry algorithms can be grouped into two main categories. The first is known as the conventional methods, and they are based on established principles of geometry. Specifically, an object’s position and orientation (pose) are obtained by identifying reference points and calculating how those points change over the image sequence. Algorithms in this category can be further divided into two: sparse feature based methods and direct methods, which differ in the method employed to select reference points. Sparse feature based methods establish reference points using image salient features such as corners and edges [8]. Direct methods, on the other hand, make use of the whole image and consider every pixel as a reference point [11]. Recently, semi-direct methods that combine the benefits of both approaches are gaining popularity [16].<br />
<br />
Today, most of the state-of-the-art VO algorithms belong to the geometry family. However, they suffer significant limitations. For example, direct methods assume “photometric consistency” [11]. Sparse feature based methods are also prone to “drifting” because of outliers and noises. As a result, the paper argues that geometry-based methods are difficult to engineer and calibrate, limiting its practicality. Figure 1 illustrates the general architecture of geometry-based algorithms and it outlines necessary drift correction techniques such as Camera Calibration, Feature Detection, Feature Matching (tracking), Outlier Rejection, Motion Estimation, Scale Estimation, and Local optimization (bundle adjustment).<br />
<br />
[[File:DeepVO_Figure_1.png | center]]<br />
<br />
<div align="center">Figure 1. Architectures of the conventional geometry-based monocular VO method.</div><br />
<br />
The second category of VO algorithms is based on learning. Namely, they try to learn an object’s motion model from labeled optical flows. Initially, these models are trained using classic Machine Learning techniques such as k-nearest neighbors (KNNs) [15], Gaussian Processes [16], and Support Vector Machines [17]. However, these models were inefficient to handle highly non-linear and high-dimensional inputs, leading to poor performance in comparison with geometry-based methods. For this reason, Deep Learning-based approaches are dominating research in this field and are producing many promising results. For example, CNN based models can now recognize places based on appearance [18] and detect direction and velocity from stereo inputs [20]. Moreover, a deep learning model even achieved robust VO with blurred and under-exposed images [21]. While these successes are encouraging, the authors observe that a CNN based architecture is “incapable of modeling sequential information.” Instead, they proposed to use RNN to tackle this problem.<br />
<br />
== End-to-End Visual odometry through RCNN ==<br />
<br />
=== Architecture Overview ===<br />
An end-to-end monocular VO model is proposed by utilizing deep Recurrence Convolutional Neural Network (RCNN). Figure 2 depicts the end-to-end model, which is comprised of three main stages. First, the model takes a monocular video as input and pre-processes the image sequences by “subtracting the mean RGB values of all frames” from each frame. Then, consecutive image sequences are stacked to form tensors, which become the inputs for the CNN stage. The purpose of the CNN stages is to extract salient features from the image tensors. The structure of the CNN is inspired by FlowNet [24], which is a model designed to extract optical flows. Details of the CNN structure is shown in Table 1. In this architecture, the size of the receptive fields in the network are gradually reduced from 7x7 to 5x5 and then to 3x3 to capture small interesting features. Zero-paddings are introduced either adapt to the configurations of receptive fields or preserve the spatial dimension of the tensor after convolution. The CNN takes raw RGB images as input. The output is a compressed respresentation of the features of optical flow. Using CNN optical flow features as input, the RNN stage tries to estimate the temporal and sequential relations among the features. The RNN stage does this by utilizing two Long Short-Term Memory networks (LSTM), which estimate object poses for each time step using both long-term and short-term dependencies. Figure 3 illustrates the RNN architecture.<br />
<br />
Without the LSTM framework, RNNs often experience vanishing gradients or gradient exploding. If the gradient is small and the network is deep, when it is propagated to the shallower layers during the backward pass, it often just becomes too small to have an effect on the weights. This forces standard RNN architectures to be relatively shallow for temporal prediction over time. In other words, the weight update for recent events will have a much larger effect on the network weights than events happened long-time ago. Visual odometry is a very complex problem, and thus we attempt to learn highly complex functions within the network. Hence, to circumvent the vanishing gradient issue, we use LSTM nodes. Conversely, LSTM can handle long-term dependencies and has deep temporal structure, but needs depth on network layers to learn complex high-level representation. LSTM define three additional gates: forget gate, input gate and update gate to help better capture the long-term dependencies. Deep RNNs have been shown to perform well on complex dynamic representations (e.g. speech recognition), and thus we leverage this architecture and layer multiple LSTM layers to mitigate vanishing gradient without losing the network's ability to represent complex dynamics.<br />
<br />
[[File:DeepVO_Figure_2.png | center]]<br />
<div align="center">Figure 2. Architectures of the proposed RCNN based monocular VO system.</div><br />
<br />
[[File:DeepVO_Table_1.png | center]]<br />
<div align="center">Table 1. CNN structure</div><br />
<br />
[[File:DeepVO_Figure_3.png | center]]<br />
<div align="center">Figure 3. Folded and unfolded LSTMs and its internal structure.</div><br />
<br />
=== Training and Optimization ===<br />
The proposed RCNN model can be represented as a conditional probability of poses <math> Y_{t} = (y_{1},...y_{t}) </math> given an image sequence <math> X_{t} = (x_{1},...x_{t}) </math>: <br />
<br />
<math><br />
p(Y_{t}|X_{t}) = p(y_{1},...,y_{t}|x_{1},...,x_{t})<br />
</math><br />
<br />
Given this probability function is expressed by a deep RCNN.<br />
To find the optimal hyperparameters, the DNN maximizes:<br />
<br />
<math><br />
\theta^{*}=argmax(Y{t}|X{t};\theta)<br />
</math><br />
<br />
To learn the hyperparameters <math>\theta</math> of the DNNs, the Euclidean distance between the ground truth pose <math>(p_k,\phi_k)</math> at time k and its estimated one <math>(\hat{p}_k,\hat{\phi}_k)</math> is minimized. the loss function that is composed of Mean Square Error (MSE) of all positions p and orientations <math>\varphi</math> minimizes:<br />
<br />
<math><br />
\theta^{*}=argmin\frac{1}{N}\sum_{N}^{i=1}\sum_{t}^{k=1}||\hat{p}_{k}-p_{k}||_{2}^{2}+\kappa||\hat{\varphi}_{k}-\varphi_{k}||_{2}^{2}<br />
</math><br />
<br />
where || *|| is <math>L_{2}-norm</math>, <math>\kappa</math> (100 in the experiments) is a scale factor to balance the weights of positions and orientations, N is the number of samples, and the orientation φ is represented by Euler angles.<br />
<br />
== Experiments and Results ==<br />
The paper evaluates the proposed RCNN VO model by comparing it empirically with the open-source VO library of LIBVISO2 [7], which is a well-known geometry based model. The comparison is done using the KITTI VO/SLAM benchmark [3], which contains 22 image sequences, 11 of which are labeled with ground truths. Two separate experiments are performed. <br />
<br />
1. Quantitatively Analysis is performed using only labeled image sequence. Namely, 4 of 11 image sequences were used for training and the others reserved for testing. Table 2 and Figure 6 outlines the result, showing that the proposed RCNN model performs consistently better than the monocular VISO2_M model. However, it performs worse than the stereo VISO2_S model.<br />
<br />
<br />
[[File:DeepVO_Table_2.png |500px| center]]<br />
<br />
<br />
[[File:DeepVO_Figure_6.png |500px| center]]<br />
<br />
<br />
2. The generalizability of the proposed RCNN model is evaluated using the unlabeled image sequences. Figure 8 outlines the test result, showing that the proposed model is able to generalize better than the monocular VISO2_M model and performs roughly the same as the stereo VISO2_S model.<br />
<br />
<br />
[[File:DeepVO_Figure_8.png |600px| center]]<br />
<br />
== Conclusions ==<br />
The paper presents a new RCNN VO model that combines the CNNs with the RNNs under the power of Deep RCNNs. It can achieve representation learning while sequential modelling of the the monocular VO. Although it is considered a viable approach, it is not expected to be a replacement to the classic geometry-based approach. However, from the experiment result, it can be a viable complement by combining geometry and DNN learning representations, knowledge and models to further improve VO's accuracy and robustness. The main contribution of the paper is threefold: <br />
<br />
# The authors demonstrate that the monocular VO problem can be addressed in an end-to-end fashion based on DL, i.e., directly estimating poses from raw RGB images. Neither prior knowledge nor parameter is needed to recover the absolute scale. <br />
#The authors propose a RCNN architecture enabling the DL based VO algorithm to be generalised to totally new environments by using the geometric feature representation learnt by the CNN. <br />
# Sequential dependence and complex motion dynamics of an image sequence, which are of importance to the VO but cannot be explicitly or easily modelled by human, are implicitly encapsulated and automatically learnt by the RCNN.<br />
<br />
== Critiques ==<br />
<br />
This paper cannot be considered as a critical advance to the state of the art as the authors just suggest a method combining CNN and RNNs for the visual odometry problem. The authors also state that deep learning in terms of simple feed-forward Neural networks and CNNs has already been used in this problem. Only an RNN approach seems to have been not tried on this problem. The authors propose a combined RCNN and geometric-based approach towards the end of the paper. But it is not intuitive how these two potentially very diverse methods could be combined. The authors also do not explain any proposed methods for the combination. The authors don't build a compelling case against the state of the art methods or convincingly prove the superiority of the RCNN or a combined method. For example, the RCNN and other state of the art geometry-based methods have a deficiency of getting lower accuracies when shown a large open area in the images as mentioned by the authors. The authors put forth some techniques to solve this problem for the geometry approaches but they state that they do not have a similar method for the deep learning based approaches. Thus, in such scenarios, the methods proposed by the authors don't seem to work at all. <br />
<br />
The paper advances the field of deep-learning based VO by creating a pioneering end-to-end model that is capable of extracting features and learning sequential dynamics from monocular videos. While the new model clearly outperforms the LIBVISO2_M algorithm, it fails to demonstrate any advantage over the LIBVISO2_S algorithm. Hence, it makes one question whether the complexity of deep-learning based monocular VO methods is justified and whether robots or autonomous vehicles designers should opt for stereo visions as much as possible. Nonetheless, this end-to-end model is beneficial for situations where monocular VO is the only viable option. Furthermore, the paper could have benefited by including a qualitative comparison of the algorithm’s computation requirements, such as hardware specification, engineering time, and training time. Though the justification for input sequence pre-processing is not explained completely, but it can be attributed to the fact that they are using standard pre-processing techniques like mean Subtraction and normalization, which helps in easier optimization of cost functions. Perhaps, future-works could involve adapting the model for real-time visual odometry.<br />
<br />
== References ==<br />
[1] S. Wang, R. Clark, H. Wen and N. Trigoni, "DeepVO: Towards end-to-end visual odometry with deep Recurrent Convolutional Neural Networks," 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 2017, pp. 2043-2050.<br />
<br />
[2] M. Maimone, Y. Cheng, and L. Matthies, "Two years of Visual Odometry on the Mars Exploration Rovers," Journal of Field Robotics. 24 (3): 169–186, 2007.<br />
<br />
[3] A. Geiger, P. Lenz, and R. Urtasun, “Are we ready for autonomous driving? the KITTI vision benchmark suite,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012.<br />
<br />
[7] A. Geiger, J. Ziegler, and C. Stiller, “Stereoscan: Dense 3D reconstruction in real-time,” in Intelligent Vehicles Symposium (IV), 2011.<br />
<br />
[8] A. J. Davison, I. D. Reid, N. D. Molton, and O. Stasse, “MonoSLAM: Real-time single camera SLAM,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 1052–1067, 2007.<br />
<br />
[11] R. A. Newcombe, S. J. Lovegrove, and A. J. Davison, “DTAM: Dense tracking and mapping in real-time,” in Proceedings of IEEE International Conference on Computer Vision (ICCV). IEEE, 2011, pp. 2320–2327.<br />
<br />
[15] R. Roberts, H. Nguyen, N. Krishnamurthi, and T. Balch, “Memory-based learning for visual odometry,” in Proceedings of IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2008, pp. 47–52.<br />
<br />
[16] V. Guizilini and F. Ramos, “Semi-parametric learning for visual odometry,” The International Journal of Robotics Research, vol. 32, no. 5, pp. 526–546, 2013.<br />
<br />
[17] T. A. Ciarfuglia, G. Costante, P. Valigi, and E. Ricci, “Evaluation of non-geometric methods for visual odometry,” Robotics and Autonomous Systems, vol. 62, no. 12, pp. 1717–1730, 2014.<br />
<br />
[18] N. Su ̈nderhauf, S. Shirazi, A. Jacobson, F. Dayoub, E. Pepperell, B. Upcroft, and M. Milford, “Place recognition with convnet landmarks: Viewpoint-robust, condition-robust, training-free,” in Proceedings of Robotics: Science and Systems (RSS), 2015.<br />
<br />
[20] A. Kendall, M. Grimes, and R. Cipolla, “Convolutional networks for real-time 6-DoF camera relocalization,” in Proceedings of International Conference on Computer Vision (ICCV), 2015.<br />
<br />
[21] G. Costante, M. Mancini, P. Valigi, and T. A. Ciarfuglia, “Exploring representation learning with CNNs for frame-to-frame ego-motion estimation,” IEEE Robotics and Automation Letters, vol. 1, no. 1, pp.18–25, 2016.<br />
<br />
[24] A. Dosovitskiy, P. Fischery, E. Ilg, C. Hazirbas, V. Golkov, P. van der Smagt, D. Cremers, T. Brox et al., “Flownet: Learning optical flow with convolutional networks,” in Proceedings of IEEE International Conference on Computer Vision (ICCV). IEEE, 2015, pp. 2758–2766.<br />
<br />
[25]http://cs231n.github.io/neural-networks-2/</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DeepVO_Towards_end_to_end_visual_odometry_with_deep_RNN&diff=42288DeepVO Towards end to end visual odometry with deep RNN2018-12-06T12:20:59Z<p>A22ravi: /* Architecture Overview */</p>
<hr />
<div>== Introduction ==<br />
Visual Odometry (VO) is a computer vision technique for estimating an object’s position and orientation from camera images. It is an important technique commonly used for “pose estimation and robot localization” with notable applications in Mars Exploration Rovers and Autonomous Vehicles [x1] [x2]. While the research field of VO is broad, this paper focuses on the topic of monocular visual odometry. Particularly, the authors examine prominent VO methods and argue that mainstream geometry based monocular VO methods should be amended with deep learning approaches. Deep Learning (DL) has recently achieved promising results in computer vision tasks but does not include the VO field, thus the paper proposes a novel deep-learning based end-to-end VO algorithm and then empirically demonstrates its viability.<br />
<br />
== Related Work ==<br />
<br />
Visual odometry algorithms can be grouped into two main categories. The first is known as the conventional methods, and they are based on established principles of geometry. Specifically, an object’s position and orientation (pose) are obtained by identifying reference points and calculating how those points change over the image sequence. Algorithms in this category can be further divided into two: sparse feature based methods and direct methods, which differ in the method employed to select reference points. Sparse feature based methods establish reference points using image salient features such as corners and edges [8]. Direct methods, on the other hand, make use of the whole image and consider every pixel as a reference point [11]. Recently, semi-direct methods that combine the benefits of both approaches are gaining popularity [16].<br />
<br />
Today, most of the state-of-the-art VO algorithms belong to the geometry family. However, they suffer significant limitations. For example, direct methods assume “photometric consistency” [11]. Sparse feature based methods are also prone to “drifting” because of outliers and noises. As a result, the paper argues that geometry-based methods are difficult to engineer and calibrate, limiting its practicality. Figure 1 illustrates the general architecture of geometry-based algorithms and it outlines necessary drift correction techniques such as Camera Calibration, Feature Detection, Feature Matching (tracking), Outlier Rejection, Motion Estimation, Scale Estimation, and Local optimization (bundle adjustment).<br />
<br />
[[File:DeepVO_Figure_1.png | center]]<br />
<br />
<div align="center">Figure 1. Architectures of the conventional geometry-based monocular VO method.</div><br />
<br />
The second category of VO algorithms is based on learning. Namely, they try to learn an object’s motion model from labeled optical flows. Initially, these models are trained using classic Machine Learning techniques such as k-nearest neighbors (KNNs) [15], Gaussian Processes [16], and Support Vector Machines [17]. However, these models were inefficient to handle highly non-linear and high-dimensional inputs, leading to poor performance in comparison with geometry-based methods. For this reason, Deep Learning-based approaches are dominating research in this field and are producing many promising results. For example, CNN based models can now recognize places based on appearance [18] and detect direction and velocity from stereo inputs [20]. Moreover, a deep learning model even achieved robust VO with blurred and under-exposed images [21]. While these successes are encouraging, the authors observe that a CNN based architecture is “incapable of modeling sequential information.” Instead, they proposed to use RNN to tackle this problem.<br />
<br />
== End-to-End Visual odometry through RCNN ==<br />
<br />
=== Architecture Overview ===<br />
An end-to-end monocular VO model is proposed by utilizing deep Recurrence Convolutional Neural Network (RCNN). Figure 2 depicts the end-to-end model, which is comprised of three main stages. First, the model takes a monocular video as input and pre-processes the image sequences by “subtracting the mean RGB values of all frames” from each frame. Then, consecutive image sequences are stacked to form tensors, which become the inputs for the CNN stage. The purpose of the CNN stages is to extract salient features from the image tensors. The structure of the CNN is inspired by FlowNet [24], which is a model designed to extract optical flows. Details of the CNN structure is shown in Table 1. In this architecture, the size of the receptive fields in the network are gradually reduced from 7x7 to 5x5 and then to 3x3 to capture small interesting features. Zero-paddings are introduced either adapt to the configurations of receptive fields or preserve the spatial dimension of the tensor after convolution. The CNN takes raw RGB images as input. The output is a compressed respresentation of the features of optical flow. Using CNN optical flow features as input, the RNN stage tries to estimate the temporal and sequential relations among the features. The RNN stage does this by utilizing two Long Short-Term Memory networks (LSTM), which estimate object poses for each time step using both long-term and short-term dependencies. Figure 3 illustrates the RNN architecture.<br />
<br />
Without the LSTM framework, RNNs often experience vanishing gradients or gradient exploding. If the gradient is small and the network is deep, when it is propagated to the shallower layers during the backward pass, it often just becomes too small to have an effect on the weights. This forces standard RNN architectures to be relatively shallow for temporal prediction over time. In other words, the weight update for recent events will have a much larger effect on the network weights than events happened long-time ago. Visual odometry is a very complex problem, and thus we attempt to learn highly complex functions within the network. Hence, to circumvent the vanishing gradient issue, we use LSTM nodes. Conversely, LSTM can handle long-term dependencies and has deep temporal structure, but needs depth on network layers to learn complex high-level representation. LSTM define three additional gates: forget gate, input gate and update gate to help better capture the long-term dependencies. Deep RNNs have been shown to perform well on complex dynamic representations (e.g. speech recognition), and thus we leverage this architecture and layer multiple LSTM layers to mitigate vanishing gradient without losing the network's ability to represent complex dynamics.<br />
<br />
[[File:DeepVO_Figure_2.png | center]]<br />
<div align="center">Figure 2. Architectures of the proposed RCNN based monocular VO system.</div><br />
<br />
[[File:DeepVO_Table_1.png | center]]<br />
<div align="center">Table 1. CNN structure</div><br />
<br />
[[File:DeepVO_Figure_3.png | center]]<br />
<div align="center">Figure 3. Folded and unfolded LSTMs and its internal structure.</div><br />
<br />
=== Training and Optimization ===<br />
The proposed RCNN model can be represented as a conditional probability of poses given an image sequence: <br />
<br />
<math><br />
p(Y_{t}|X_{t}) = p(y_{1},...,y_{t}|x_{1},...,x_{t})<br />
</math><br />
<br />
Given this probability function is expressed by a deep RCNN.<br />
To find the optimal hyperparameters, the DNN maximizes:<br />
<br />
<math><br />
\theta^{*}=argmax(Y{t}|X{t};\theta)<br />
</math><br />
<br />
To learn the hyperparameters <math>\theta</math> of the DNNs, the Euclidean distance between the ground truth pose <math>(p_k,\phi_k)</math> at time k and its estimated one <math>(\hat{p}_k,\hat{\phi}_k)</math> is minimized. the loss function that is composed of Mean Square Error (MSE) of all positions p and orientations <math>\varphi</math> minimizes:<br />
<br />
<math><br />
\theta^{*}=argmin\frac{1}{N}\sum_{N}^{i=1}\sum_{t}^{k=1}||\hat{p}_{k}-p_{k}||_{2}^{2}+\kappa||\hat{\varphi}_{k}-\varphi_{k}||_{2}^{2}<br />
</math><br />
<br />
where || *|| is <math>L_{2}-norm</math>, <math>\kappa</math> (100 in the experiments) is a scale factor to balance the weights of positions and orientations, N is the number of samples, and the orientation φ is represented by Euler angles.<br />
<br />
== Experiments and Results ==<br />
The paper evaluates the proposed RCNN VO model by comparing it empirically with the open-source VO library of LIBVISO2 [7], which is a well-known geometry based model. The comparison is done using the KITTI VO/SLAM benchmark [3], which contains 22 image sequences, 11 of which are labeled with ground truths. Two separate experiments are performed. <br />
<br />
1. Quantitatively Analysis is performed using only labeled image sequence. Namely, 4 of 11 image sequences were used for training and the others reserved for testing. Table 2 and Figure 6 outlines the result, showing that the proposed RCNN model performs consistently better than the monocular VISO2_M model. However, it performs worse than the stereo VISO2_S model.<br />
<br />
<br />
[[File:DeepVO_Table_2.png |500px| center]]<br />
<br />
<br />
[[File:DeepVO_Figure_6.png |500px| center]]<br />
<br />
<br />
2. The generalizability of the proposed RCNN model is evaluated using the unlabeled image sequences. Figure 8 outlines the test result, showing that the proposed model is able to generalize better than the monocular VISO2_M model and performs roughly the same as the stereo VISO2_S model.<br />
<br />
<br />
[[File:DeepVO_Figure_8.png |600px| center]]<br />
<br />
== Conclusions ==<br />
The paper presents a new RCNN VO model that combines the CNNs with the RNNs under the power of Deep RCNNs. It can achieve representation learning while sequential modelling of the the monocular VO. Although it is considered a viable approach, it is not expected to be a replacement to the classic geometry-based approach. However, from the experiment result, it can be a viable complement by combining geometry and DNN learning representations, knowledge and models to further improve VO's accuracy and robustness. The main contribution of the paper is threefold: <br />
<br />
# The authors demonstrate that the monocular VO problem can be addressed in an end-to-end fashion based on DL, i.e., directly estimating poses from raw RGB images. Neither prior knowledge nor parameter is needed to recover the absolute scale. <br />
#The authors propose a RCNN architecture enabling the DL based VO algorithm to be generalised to totally new environments by using the geometric feature representation learnt by the CNN. <br />
# Sequential dependence and complex motion dynamics of an image sequence, which are of importance to the VO but cannot be explicitly or easily modelled by human, are implicitly encapsulated and automatically learnt by the RCNN.<br />
<br />
== Critiques ==<br />
<br />
This paper cannot be considered as a critical advance to the state of the art as the authors just suggest a method combining CNN and RNNs for the visual odometry problem. The authors also state that deep learning in terms of simple feed-forward Neural networks and CNNs has already been used in this problem. Only an RNN approach seems to have been not tried on this problem. The authors propose a combined RCNN and geometric-based approach towards the end of the paper. But it is not intuitive how these two potentially very diverse methods could be combined. The authors also do not explain any proposed methods for the combination. The authors don't build a compelling case against the state of the art methods or convincingly prove the superiority of the RCNN or a combined method. For example, the RCNN and other state of the art geometry-based methods have a deficiency of getting lower accuracies when shown a large open area in the images as mentioned by the authors. The authors put forth some techniques to solve this problem for the geometry approaches but they state that they do not have a similar method for the deep learning based approaches. Thus, in such scenarios, the methods proposed by the authors don't seem to work at all. <br />
<br />
The paper advances the field of deep-learning based VO by creating a pioneering end-to-end model that is capable of extracting features and learning sequential dynamics from monocular videos. While the new model clearly outperforms the LIBVISO2_M algorithm, it fails to demonstrate any advantage over the LIBVISO2_S algorithm. Hence, it makes one question whether the complexity of deep-learning based monocular VO methods is justified and whether robots or autonomous vehicles designers should opt for stereo visions as much as possible. Nonetheless, this end-to-end model is beneficial for situations where monocular VO is the only viable option. Furthermore, the paper could have benefited by including a qualitative comparison of the algorithm’s computation requirements, such as hardware specification, engineering time, and training time. Though the justification for input sequence pre-processing is not explained completely, but it can be attributed to the fact that they are using standard pre-processing techniques like mean Subtraction and normalization, which helps in easier optimization of cost functions. Perhaps, future-works could involve adapting the model for real-time visual odometry.<br />
<br />
== References ==<br />
[1] S. Wang, R. Clark, H. Wen and N. Trigoni, "DeepVO: Towards end-to-end visual odometry with deep Recurrent Convolutional Neural Networks," 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 2017, pp. 2043-2050.<br />
<br />
[2] M. Maimone, Y. Cheng, and L. Matthies, "Two years of Visual Odometry on the Mars Exploration Rovers," Journal of Field Robotics. 24 (3): 169–186, 2007.<br />
<br />
[3] A. Geiger, P. Lenz, and R. Urtasun, “Are we ready for autonomous driving? the KITTI vision benchmark suite,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012.<br />
<br />
[7] A. Geiger, J. Ziegler, and C. Stiller, “Stereoscan: Dense 3D reconstruction in real-time,” in Intelligent Vehicles Symposium (IV), 2011.<br />
<br />
[8] A. J. Davison, I. D. Reid, N. D. Molton, and O. Stasse, “MonoSLAM: Real-time single camera SLAM,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 1052–1067, 2007.<br />
<br />
[11] R. A. Newcombe, S. J. Lovegrove, and A. J. Davison, “DTAM: Dense tracking and mapping in real-time,” in Proceedings of IEEE International Conference on Computer Vision (ICCV). IEEE, 2011, pp. 2320–2327.<br />
<br />
[15] R. Roberts, H. Nguyen, N. Krishnamurthi, and T. Balch, “Memory-based learning for visual odometry,” in Proceedings of IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2008, pp. 47–52.<br />
<br />
[16] V. Guizilini and F. Ramos, “Semi-parametric learning for visual odometry,” The International Journal of Robotics Research, vol. 32, no. 5, pp. 526–546, 2013.<br />
<br />
[17] T. A. Ciarfuglia, G. Costante, P. Valigi, and E. Ricci, “Evaluation of non-geometric methods for visual odometry,” Robotics and Autonomous Systems, vol. 62, no. 12, pp. 1717–1730, 2014.<br />
<br />
[18] N. Su ̈nderhauf, S. Shirazi, A. Jacobson, F. Dayoub, E. Pepperell, B. Upcroft, and M. Milford, “Place recognition with convnet landmarks: Viewpoint-robust, condition-robust, training-free,” in Proceedings of Robotics: Science and Systems (RSS), 2015.<br />
<br />
[20] A. Kendall, M. Grimes, and R. Cipolla, “Convolutional networks for real-time 6-DoF camera relocalization,” in Proceedings of International Conference on Computer Vision (ICCV), 2015.<br />
<br />
[21] G. Costante, M. Mancini, P. Valigi, and T. A. Ciarfuglia, “Exploring representation learning with CNNs for frame-to-frame ego-motion estimation,” IEEE Robotics and Automation Letters, vol. 1, no. 1, pp.18–25, 2016.<br />
<br />
[24] A. Dosovitskiy, P. Fischery, E. Ilg, C. Hazirbas, V. Golkov, P. van der Smagt, D. Cremers, T. Brox et al., “Flownet: Learning optical flow with convolutional networks,” in Proceedings of IEEE International Conference on Computer Vision (ICCV). IEEE, 2015, pp. 2758–2766.<br />
<br />
[25]http://cs231n.github.io/neural-networks-2/</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=a_neural_representation_of_sketch_drawings&diff=42272a neural representation of sketch drawings2018-12-05T13:24:13Z<p>A22ravi: /* Related Work */</p>
<hr />
<div><br />
== Introduction ==<br />
In this paper, the authors present a recurrent neural network, sketch-rnn, that can be used to construct stroke-based drawings. Besides new robust training methods, they also outline a framework for conditional and unconditional sketch generation.<br />
<br />
Neural networks have been heavily used as image generation tools. For example, Generative Adversarial Networks, Variational Inference, and Autoregressive models have been used. Most of those models are designed to generate pixels to construct images. However, people learn to draw using sequences of strokes, beginning when they are young. The authors propose a new generative model that creates vector images so that it might generalize abstract concepts in a manner more similar to how humans do. <br />
<br />
The model is trained with hand-drawn sketches as input sequences. The model is able to produce sketches in vector format. In the conditional generation model, they also explore the latent space representation for vector images and discuss a few future applications of this model. The model and dataset are now available as an open source project ([https://magenta.tensorflow.org/sketch_rnn link]).<br />
<br />
=== Terminology ===<br />
Pixel images, also referred to as raster or bitmap images are files that encode image data as a set of pixels. These are the most common image type, with extensions such as .png, .jpg, .bmp. <br />
<br />
Vector images are files that encode image data as paths between points. SVG and EPS file types are used to store vector images. <br />
<br />
For a visual comparison of raster and vector images, see this [https://www.youtube.com/watch?v=-Fs2t6P5AjY video]. As mentioned, vector images are generally simpler and more abstract, whereas raster images generally are used to store detailed images. <br />
<br />
For this paper, the important distinction between the two is that the encoding of images in the model will be inherently more abstract because of the vector representation. The intuition is that generating abstract representations is more effective using a vector representation. <br />
<br />
== Related Work ==<br />
There are some works in the history that used a similar approach to generate images such as Portrait Drawing by Paul the Robot [26, 28] and some reinforcement learning approaches[28], Reinforcement Learning to discover a set of paint brush strokes that can best represent a given input photograph. They work more like a mimic of digitized photographs. There are also some Neural networks based approaches, but those are mostly dealing with pixel images. Little work is done on vector images generation. There are models that use Hidden Markov Models [25] or Mixture Density Networks [2] to generate human sketches, continuous data points (modelling Chinese characters as a sequence of pen stroke actions) or vectorized Kanji characters [9,29].<br />
<br />
Neural Network-based approaches are able to generate latent space representation of vector images, which follows a Gaussian distribution. The generated output of these networks is trained to match the Gaussian distribution by minimizing a given loss function. Using this idea, previous works attempted to generate a sequence-to-Sequence model with Variational Autoencoder to model sentences into latent space and using probabilistic program induction to model Omniglot dataset.<br />
<br />
One of the limiting factors that the authors mention in the field of generative vector drawings is the lack of availability of publicly available datasets. Previous datasets such as the Sketch data with 20k vector sketches was explored for feature extraction techniques. The Sketchy dataset consisting of 70k vector sketches along with pixel images was used for large-scale exploration of human sketches. The ShadowDraw system that used 30k raster images along with extracted vectorized features is an interactive system<br />
that predicts what a finished drawing looks like based on a set of incomplete brush strokes from the<br />
user while the sketch is being drawn. In all the cases, the datasets are comparatively small. The dataset proposed in this work uses a much larger dataset and has been made publicly available, and is one of the major contributions of this paper.<br />
<br />
== Major Contributions ==<br />
This paper makes the following major contributions: Authors outline a framework for both unconditional and<br />
conditional generation of vector images composed of a sequence of lines. The recurrent neural<br />
network-based generative model is capable of producing sketches of common objects in a vector<br />
format. The paper develops a training procedure unique to vector images to make the training more robust. The paper also made available<br />
a large dataset of hand drawn vector images to encourage further development of generative modelling<br />
for vector images, and also release an implementation of our model as an open source project<br />
<br />
== Methodology ==<br />
=== Dataset ===<br />
QuickDraw is a dataset with 50 million vector drawings collected by an online game [https://quickdraw.withgoogle.com/# Quick Draw!], where the players are required to draw objects belonging to a particular object class in less than 20 seconds. It contains hundreds of classes, each class has 70k training samples, 2.5k validation samples and 2.5k test samples.<br />
<br />
The data format of each sample is a representation of a pen stroke action event. The Origin is the initial coordinate of the drawing. The sketches are points in a list. Each point consists of 5 elements <math> (\Delta x, \Delta y, p_{1}, p_{2}, p_{3})</math> where x and y are the offset distance in x and y directions from the previous point. The parameters <math>p_{1}, p_{2}, p_{3}</math> represent three possible states in binary one-hot representation where <math>p_{1}</math> indicates the pen is touching the paper, <math>p_{2}</math> indicates the pen will be lifted from here, and <math>p_{3}</math> represents the drawing has ended.<br />
<br />
=== Sketch-RNN ===<br />
[[File:sketchfig2.png|700px|center]]<br />
<br />
The model is a Sequence-to-Sequence Variational Autoencoder(VAE). <br />
<br />
==== Encoder ====<br />
The encoder is a bidirectional RNN. The input is a sketch sequence denoted by <math>S =\{S_0, S_1, ... S_{N_{s}}\}</math> and a reversed sketch sequence denoted by <math>S_{reverse} = \{S_{N_{s}},S_{N_{s}-1}, ... S_0\}</math>. The final hidden layer representations of the two encoded sequences <math>(h_{ \rightarrow}, h_{ \leftarrow})</math> are concatenated to form a latent vector, <math>h</math>, of size <math>N_{z}</math>,<br />
<br />
\begin{split}<br />
&h_{ \rightarrow} = encode_{ \rightarrow }(S), \\<br />
&h_{ \leftarrow} = encode_{ \leftarrow }(S_{reverse}), \\<br />
&h = [h_{\rightarrow}; h_{\leftarrow}].<br />
\end{split}<br />
<br />
Then the authors project <math>h</math> into two vectors <math>\mu</math> and <math>\hat{\sigma}</math> of size <math>N_{z}</math>. The projection is performed using a fully connected layer. These two vectors are the parameters of the latent space Gaussian distribution that will estimate the distribution of the input data. Because standard deviations cannot be negative, an exponential function is used to convert it to all positive values. Next, a random variable with mean <math>\mu</math> and standard deviation <math>\sigma</math> is constructed by scaling a normalized IID Gaussian, <math>\mathcal{N}(0,I)</math>, <br />
<br />
\begin{split}<br />
& \mu = W_\mu h + b_\mu, \\<br />
& \hat \sigma = W_\sigma h + b_\sigma, \\<br />
& \sigma = exp( \frac{\hat \sigma}{2}), \\<br />
& z = \mu + \sigma \odot \mathcal{N}(0,I). <br />
\end{split}<br />
<br />
<br />
Note that <math>z</math> is not deterministic but a random vector that can be conditioned on an input sketch sequence.<br />
<br />
==== Decoder ====<br />
The decoder is an autoregressive RNN. The initial hidden and cell states are generated using <math>[h_0;c_0] = \tanh(W_z z + b_z)</math>. Here, <math>c_0</math> is utilized if applicable (eg. if an LSTM decoder is used). <math>S_0</math> is defined as <math>(0,0,1,0,0)</math> (the pen is touching the paper at location 0, 0). <br />
<br />
For each step <math>i</math> in the decoder, the input <math>x_i</math> is the concatenation of the previous point <math>S_{i-1}</math> and the latent vector <math>z</math>. The outputs of the RNN decoder <math>y_i</math> are parameters for a probability distribution that will generate the next point <math>S_i</math>. <br />
<br />
The authors model <math>(\Delta x,\Delta y)</math> as a Gaussian mixture model (GMM) with <math>M</math> normal distributions and model the ground truth data <math>(p_1, p_2, p_3)</math> as a categorical distribution <math>(q_1, q_2, q_3)</math> where <math>q_1, q_2\ \text{and}\ q_3</math> sum up to 1,<br />
<br />
\begin{align*}<br />
p(\Delta x, \Delta y) = \sum_{j=1}^{M} \Pi_j \mathcal{N}(\Delta x,\Delta y | \mu_{x,j}, \mu_{y,j}, \sigma_{x,j},\sigma_{y,j}, \rho _{xy,j}), where \sum_{j=1}^{M}\Pi_j = 1<br />
\end{align*}<br />
<br />
Where <math>\mathcal{N}(\Delta x,\Delta y | \mu_{x,j}, \mu_{y,j}, \sigma_{x,j},\sigma_{y,j}, \rho _{xy,j})</math> is a bi-variate Normal Distribution, with parameters means <math>\mu_x, \mu_y</math>, standard deviations <math>\sigma_x, \sigma_y</math> and correlation parameter <math>\rho_{xy}</math>. There are <math>M</math> such distributions. <math>\Pi</math> is a categorical distribution vector of length <math>M</math>. Collectively these form the mixture weights of the Gaussian Mixture model.<br />
<br />
The output vector <math>y_i</math> is generated using a fully-connected forward propagation in the hidden state of the RNN.<br />
<br />
\begin{split}<br />
&x_i = [S_{i-1}; z], \\<br />
&[h_i; c_i] = forward(x_i,[h_{i-1}; c_{i-1}]), \\<br />
&y_i = W_y h_i + b_y, \\<br />
&y_i \in \mathbb{R}^{6M+3}. \\<br />
\end{split}<br />
<br />
The output consists the probability distribution of the next data point.<br />
<br />
\begin{align*}<br />
[(\hat\Pi_1\ \mu_x\ \mu_y\ \hat\sigma_x\ \hat\sigma_y\ \hat\rho_{xy})_1\ (\hat\Pi_1\ \mu_x\ \mu_y\ \hat\sigma_x\ \hat\sigma_y\ \hat\rho_{xy})_2\ ...\ (\hat\Pi_1\ \mu_x\ \mu_y\ \hat\sigma_x\ \hat\sigma_y\ \hat\rho_{xy})_M\ (\hat{q_1}\ \hat{q_2}\ \hat{q_3})] = y_i<br />
\end{align*}<br />
<br />
<math>\exp</math> and <math>\tanh</math> operations are applied to ensure that the standard deviations are non-negative and the correlation value is between -1 and 1.<br />
<br />
\begin{align*}<br />
\sigma_x = \exp (\hat \sigma_x),\ <br />
\sigma_y = \exp (\hat \sigma_y),\ <br />
\rho_{xy} = \tanh(\hat \rho_{xy}). <br />
\end{align*}<br />
<br />
Categorical distribution probabilities for <math>(p_1, p_2, p_3)</math> using <math>(q_1, q_2, q_3)</math> can be obtained as :<br />
<br />
\begin{align*}<br />
q_k = \frac{\exp{(\hat q_k)}}{ \sum\nolimits_{j = 1}^{3} \exp {(\hat q_j)}},<br />
k \in \left\{1,2,3\right\}, <br />
\Pi _k = \frac{\exp{(\hat \Pi_k)}}{ \sum\nolimits_{j = 1}^{M} \exp {(\hat \Pi_j)}},<br />
k \in \left\{1,...,M\right\}.<br />
\end{align*}<br />
<br />
It is hard for the model to decide when to stop drawing because the probabilities of the three events <math>(p_1, p_2, p_3)</math> are very unbalanced. Researchers in the past have used different weights for each pen event probability, but the authors found this approach lacking elegance and inadequate. They define a hyperparameter representing the max length of the longest sketch in the training set denoted by <math>N_{max}</math>, and set the <math>S_i</math> to be <math>(0, 0, 0, 0, 1)</math> for <math>i > N_s</math>.<br />
<br />
The outcome sample <math>S_i^{'}</math> can be generated in each time step during sample process and fed as input for the next time step. The process will stop when <math>p_3 = 1</math> or <math>i = N_{max}</math>. The output is not deterministic but conditioned random sequences. The level of randomness can be controlled using a temperature parameter <math>\tau</math>.<br />
<br />
\begin{align*}<br />
\hat q_k \rightarrow \frac{\hat q_k}{\tau}, <br />
\hat \Pi_k \rightarrow \frac{\hat \Pi_k}{\tau}, <br />
\sigma_x^2 \rightarrow \sigma_x^2\tau, <br />
\sigma_y^2 \rightarrow \sigma_y^2\tau. <br />
\end{align*}<br />
<br />
The <math>\tau</math> ranges from 0 to 1. When <math>\tau = 0</math> the output will be deterministic as the sample will consist of the points on the peak of the probability density function.<br />
<br />
=== Unconditional Generation ===<br />
There is a special case that only the decoder RNN module is trained. The decoder RNN could work as a standalone autoregressive model without latent variables. In this case, initial states are 0, the input <math>x_i</math> is only <math>S_{i-1}</math> or <math>S_{i-1}^{'}</math>. In the Figure 3, generating sketches unconditionally from the temperature parameter <math>\tau = 0.2</math> at the top in blue, to <math>\tau = 0.9</math> at the bottom in red.<br />
<br />
[[File:sketchfig3.png|700px|center]]<br />
<br />
=== Training ===<br />
The training process is the same as a Variational Autoencoder. The loss function is the sum of Reconstruction Loss <math>L_R</math> and the Kullback-Leibler Divergence Loss <math>L_{KL}</math>. The reconstruction loss <math>L_R</math> can be obtained with generated parameters of pdf and training data <math>S</math>. It is the sum of the <math>L_s</math> and <math>L_p</math>, which are the log loss of the offset <math>(\Delta x, \Delta y)</math> and the pen state <math>(p_1, p_2, p_3)</math>.<br />
<br />
\begin{align*}<br />
L_s = - \frac{1 }{N_{max}} \sum_{i = 1}^{N_s} \log(\sum_{i = 1}^{M} \Pi_{j,i} \mathcal{N}(\Delta x,\Delta y | \mu_{x,j,i}, \mu_{y,j,i}, \sigma_{x,j,i},\sigma_{y,j,i}, \rho _{xy,j,i})), <br />
\end{align*}<br />
\begin{align*}<br />
L_p = - \frac{1 }{N_{max}} \sum_{i = 1}^{N_{max}} \sum_{k = 1}^{3} p_{k,i} \log (q_{k,i}), <br />
L_R = L_s + L_p.<br />
\end{align*}<br />
<br />
<br />
Both terms are normalized by <math>N_{max}</math>.<br />
<br />
<math>L_{KL}</math> measures the difference between the distribution of the latent vector <math>z</math> and an i.i.d. Gaussian vector with zero mean and unit variance.<br />
<br />
\begin{align*}<br />
L_{KL} = - \frac{1}{2 N_z} (1+\hat \sigma - \mu^2 - \exp(\hat \sigma))<br />
\end{align*}<br />
<br />
The overall loss is weighted as:<br />
<br />
\begin{align*}<br />
Loss = L_R + w_{KL} L_{KL}<br />
\end{align*}<br />
<br />
When <math>w_{KL} = 0</math>, the model becomes a standalone unconditional generator. Specially, there will be no <math>L_{KL} </math> term as we only optimize for <math>L_{R} </math>. By removing the <math>L_{KL} </math> term the model approaches a pure autoencoder, meaning it sacrifices the ability to enforce a prior over the latent space and gains better reconstruction loss metrics.<br />
<br />
While the aforementioned loss function could be used, it was found that annealing the KL term (as shown below) in the loss function produces better results.<br />
<br />
<center><math><br />
\eta_{step} = 1 - (1 - \eta_{min})R^{step}<br />
</math></center><br />
<br />
<center><math><br />
Loss_{train} = L_R + w_{KL} \eta_{step} max(L_{KL}, KL_{min})<br />
</math></center><br />
<br />
As shown in Figure 4, the <math>L_{R} </math> metric for the standalone decoder model is actually an upper bound for different models using a latent vector. The reason is the unconditional model does not access to the entire sketch it needs to generate.<br />
<br />
[[File:s.png|600px|thumb|center|Figure 4. Tradeoff between <math>L_{R} </math> and <math>L_{KL} </math>, for two models trained on single class datasets (left).<br />
Validation Loss Graph for models trained on the Yoga dataset using various <math>w_{KL} </math>. (right)]]<br />
<br />
== Experiments ==<br />
The authors experiment with the sketch-rnn model using different settings and recorded both losses. They used a Long Short-Term Memory(LSTM) model as an encoder and a HyperLSTM as a decoder. HyperLSTM is a type of RNN cell that excels at sequence generation tasks. The ability for HyperLSTM to spontaneously augment its own weights enables it to adapt to many different regimes<br />
in a large diverse dataset. They also conduct multi-class datasets. The result is as follows.<br />
<br />
[[File:sketchtable1.png|700px|center]]<br />
<br />
We could see the trade-off between <math>L_R</math> and <math>L_{KL}</math> in this table clearly. Furthermore, <math>L_R</math> decreases as <math>w_{KL} </math> is halfed. <br />
<br />
=== Conditional Reconstruction ===<br />
The authors assess the reconstructed sketch with a given sketch with different <math>\tau</math> values. We could see that with high <math>\tau</math> value on the right, the reconstructed sketches are more random.<br />
<br />
[[File:sketchfig5.png|700px|center]]<br />
<br />
They also experiment on inputting a sketch from a different class. The output will still keep some features from the class that the model is trained on.<br />
<br />
=== Latent Space Interpolation ===<br />
The authors visualize the reconstruction sketches while interpolating between latent vectors using different <math>w_{KL}</math> values. With high <math>w_{KL}</math> values, the generated images are more coherently interpolated.<br />
<br />
[[File:sketchfig6.png|700px|center]]<br />
<br />
=== Sketch Drawing Analogies ===<br />
Since the latent vector <math>z</math> encode conceptual features of a sketch, those features can also be used to augment other sketches that do not have these features. This is possible when models are trained with low <math>L_{KL}</math> values. The authors are able to perform vector arithmetic on latent vectors from different sketches and explore how the model generates sketches base on these latent spaces.<br />
<br />
=== Predicting Different Endings of Incomplete Sketches === <br />
This model is able to predict an incomplete sketch by encoding the sketch into hidden state <math>h</math> using the decoder and then using <math>h</math> as an initial hidden state to generate the remaining sketch. The authors train on individual classes by using decoder-only models and set <math>τ = 0.8</math> to complete samples. Figure 7 shows the results.<br />
<br />
[[File:sketchfig7.png|700px|center]]<br />
<br />
== Limitations ==<br />
<br />
Although sketch-rnn can model a large variety of sketch drawings, there are several limitations in the current approach. For most single-class datasets, sketch-rnn is capable of modelling around 300 data points. The model becomes increasingly difficult to train beyond this length. For the author's dataset, the Ramer-Douglas-Peucker algorithm is used to simplify the strokes of sketch data to less than 200 data points.<br />
<br />
For more complicated classes of images, such as mermaids or lobsters, the reconstruction loss metrics are not as good compared to simpler classes such as ants, faces or firetrucks. The models trained on these more challenging image classes tend to draw smoother, more circular line segments that do not resemble individual sketches, but rather resemble an averaging of many sketches in the training set. This smoothness may be analogous to the blurriness effect produced by a Variational Autoencoder that is trained on pixel images. Depending on the use case of the model, smooth circular lines can be viewed as aesthetically pleasing and a desirable property.<br />
<br />
While both conditional and unconditional models are capable of training on datasets of several classes, sketch-rnn is ineffective at modelling a large number of classes simultaneously. The samples generated will be incoherent, with different classes are shown in the same sketch.<br />
<br />
== Applications and Future Work ==<br />
The authors believe this model can assist artists by suggesting how to finish a sketch, helping them to find interesting intersections between different drawings or objects, or generating a lot of similar but different designs. In the simplest use, pattern designers can apply sketch-rnn to generate a large number of similar, but unique designs for textile or wallpaper prints. The creative designers can also come up with abstract designs which enables them to resonate more with their target audience<br />
<br />
This model may also find its place on teaching students how to draw. Even with the simple sketches in QuickDraw, the authors of this work have become much more proficient at drawing animals, insects, and various sea creatures after conducting these experiments. <br />
When the model is trained with a high <math>w_{KL}</math> and sampled with a low <math>\tau</math>, it may help to turn a poor sketch into a more aesthetical one. Latent vector augmentation could also help to create a better drawing by inputting user-rating data during training processes.<br />
<br />
The authors conclude by providing the following future directions to this work:<br />
# Investigate using user-rating data to augmenting the latent vector in the direction that maximizes the aesthetics of the drawing.<br />
# Look into combining variations of sequence-generation models with unsupervised, cross-domain pixel image generation models.<br />
<br />
It's exciting that they manage to combine this model with other unsupervised, cross-domain pixel image generation models to create photorealistic images from sketches.<br />
<br />
The authors have also mentioned the opposite direction of converting a photograph of an object into an unrealistic, but similar looking<br />
sketch of the object composed of a minimal number of lines to be a more interesting problem.<br />
<br />
Moreover, it would be interesting to see how varying loss will be represented as a drawing. Some exotic form of loss function may change the way that the network behaves, which can lead to various applications.<br />
<br />
== Conclusion ==<br />
The paper presents a methodology to model sketch drawings using recurrent neural networks. The sketch-rnn model that can encode and decode sketches, generate and complete unfinished sketches is introduced in this paper. In addition, Authors demonstrated how to both interpolate between latent spaces from a different class, and use it to augment sketches or generate similar looking sketches. Furthermore, the importance of enforcing a prior distribution on latent vector while interpolating coherent sketch generations is shown. Finally, a large sketch drawings dataset for future research work is created.<br />
<br />
== Critique ==<br />
This paper presents both a novel large dataset of sketches and a new RNN architecture to generate new sketches. It is very exciting to read but there are still some aspect to improve.<br />
<br />
* The performance of the decoder model can hardly be evaluated. The authors present the performance of the decoder by showing the generated sketches, it is clear and straightforward, however, not very efficient. It would be great if the authors could present a way, or a metric to evaluate how well the sketches are generated rather than printing them out and evaluate with human judgment. The authors didn't present an evaluation of the algorithms either. They provided <math>L_R</math> and <math>L_{KL}</math> for reference, however, a lower loss doesn't represent a better performance. Training loss alone likely does not capture the quality of a sketch.<br />
<br />
* The authors have not mentioned details on training details such as learning rate, training time, parameter size, and so on. <br />
<br />
* Algorithm lacks comparison to the prior state of the art on standard metrics, which made the novelty unclear. Using strokes as inputs is a novel and innovative move, however, the paper does not provide a baseline or any comparison with other methods or algorithms. Some other researches were mentioned in the paper, using similar and smaller datasets. It would be great if the authors could use some basic or existing methods a baseline and compare with the new algorithm.<br />
<br />
* Besides the comparison with other algorithms, it would also be great if the authors could remove or replace some component of the algorithm in the model to show if one part is necessary, or what made them decide to include a specific component in the algorithm.<br />
<br />
* The authors did not present better complexity and deeper mathematical analysis on the algorithms in the paper. It also does not include comparison using some more standard metrics compare to previous results. Therefore, it lacks some algorithmic contribution. It would be better to include some more formal analysis on the algorithmic side. <br />
<br />
* The authors proposed a few future applications for the model, however, the current output seems somehow not very close to their descriptions. But I do believe that this is a very good beginning, with the release of the sketch dataset, it must attract more scholars to research and improve with it!<br />
<br />
* As they said their model can become increasingly difficult to train on with increased size.<br />
<br />
== References == <br />
# Jimmy L. Ba, Jamie R. Kiros, and Geoffrey E. Hinton. Layer normalization. NIPS, 2016.<br />
# Christopher M. Bishop. Mixture density networks. Technical Report, 1994. URL http://publications.aston.ac.uk/373/.<br />
# Samuel R. Bowman, Luke Vilnis, Oriol Vinyals, Andrew M. Dai, Rafal Józefowicz, and Samy Bengio. Generating Sentences from a Continuous Space. CoRR, abs/1511.06349, 2015. URL http://arxiv.org/abs/1511.06349.<br />
# H. Dong, P. Neekhara, C. Wu, and Y. Guo. Unsupervised Image-to-Image Translation with Generative Adversarial Networks. ArXiv e-prints, January 2017.<br />
# David H. Douglas and Thomas K. Peucker. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2):112–122, October 1973. doi: 10.3138/fm57-6770-u75u-7727. URL http://dx.doi.org/10.3138/fm57-6770-u75u-7727.<br />
# Mathias Eitz, James Hays, and Marc Alexa. How Do Humans Sketch Objects? ACM Trans. Graph.(Proc. SIGGRAPH), 31(4):44:1–44:10, 2012.<br />
# I. Goodfellow. NIPS 2016 Tutorial: Generative Adversarial Networks. ArXiv e-prints, December 2016.<br />
# Alex Graves. Generating sequences with recurrent neural networks. arXiv:1308.0850, 2013.<br />
# David Ha. Recurrent Net Dreams Up Fake Chinese Characters in Vector Format with TensorFlow, 2015.<br />
# David Ha, Andrew M. Dai, and Quoc V. Le. HyperNetworks. In ICLR, 2017.<br />
# Sepp Hochreiter and Juergen Schmidhuber. Long short-term memory. Neural Computation, 1997.<br />
# P. Isola, J.-Y. Zhu, T. Zhou, and A. A. Efros. Image-to-Image Translation with Conditional Adversarial Networks. ArXiv e-prints, November 2016.<br />
# Jonas Jongejan, Henry Rowley, Takashi Kawashima, Jongmin Kim, and Nick Fox-Gieg. The Quick, Draw! - A.I. Experiment. https://quickdraw.withgoogle.com/, 2016. URL https: //quickdraw.withgoogle.com/.<br />
# C. Kaae Sønderby, T. Raiko, L. Maaløe, S. Kaae Sønderby, and O. Winther. Ladder Variational Autoencoders. ArXiv e-prints, February 2016.<br />
# T. Kim, M. Cha, H. Kim, J. Lee, and J. Kim. Learning to Discover cross-domain Relations with Generative Adversarial Networks. ArXiv e-prints, March 2017.<br />
# D. P Kingma and M. Welling. Auto-Encoding Variational Bayes. ArXiv e-prints, December 2013.<br />
# Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.<br />
# Diederik P. Kingma, Tim Salimans, and Max Welling. Improving variational inference with inverse autoregressive flow. CoRR, abs/1606.04934, 2016. URL http://arxiv.org/abs/1606.04934.<br />
# Brenden M. Lake, Ruslan Salakhutdinov, and Joshua B. Tenenbaum. Human level concept learning through probabilistic program induction. Science, 350(6266):1332–1338, December 2015. ISSN 1095-9203. doi: 10.1126/science.aab3050. URL http://dx.doi.org/10.1126/science.aab3050.<br />
# Yong Jae Lee, C. Lawrence Zitnick, and Michael F. Cohen. Shadowdraw: Real-time user guidance for freehand drawing. In ACM SIGGRAPH 2011 Papers, SIGGRAPH ’11, pp. 27:1–27:10, New York, NY, USA, 2011. ACM. ISBN 978-1-4503-0943-1. doi: 10.1145/1964921.1964922. URL http://doi.acm.org/10.1145/1964921.1964922.<br />
# M.-Y. Liu, T. Breuel, and J. Kautz. Unsupervised Image-to-Image Translation Networks. ArXiv e-prints, March 2017.<br />
# S. Reed, A. van den Oord, N. Kalchbrenner, S. Gómez Colmenarejo, Z. Wang, D. Belov, and N. de Freitas. Parallel Multiscale Autoregressive Density Estimation. ArXiv e-prints, March 2017.<br />
# Patsorn Sangkloy, Nathan Burnell, Cusuh Ham, and James Hays. The Sketchy Database: Learning to Retrieve Badly Drawn Bunnies. ACM Trans. Graph., 35(4):119:1–119:12, July 2016. ISSN 0730-0301. doi: 10.1145/2897824.2925954. URL http://doi.acm.org/10.1145/2897824.2925954.<br />
# Mike Schuster, Kuldip K. Paliwal, and A. General. Bidirectional recurrent neural networks. IEEE Transactions on Signal Processing, 1997.<br />
# Saul Simhon and Gregory Dudek. Sketch interpretation and refinement using statistical models. In Proceedings of the Fifteenth Eurographics Conference on Rendering Techniques, EGSR’04, pp. 23–32, Aire-la-Ville, Switzerland, Switzerland, 2004. Eurographics Association. ISBN 3-905673-12-6. doi: 10.2312/EGWR/EGSR04/023-032. URL http://dx.doi.org/10.2312/EGWR/EGSR04/023-032.<br />
# Patrick Tresset and Frederic Fol Leymarie. Portrait drawing by paul the robot. Comput. Graph.,37(5):348–363, August 2013. ISSN 0097-8493. doi: 10.1016/j.cag.2013.01.012. URL http://dx.doi.org/10.1016/j.cag.2013.01.012.<br />
# T. White. Sampling Generative Networks. [https://arxiv.org/abs/1609.04468 ArXiv e-prints], September 2016.<br />
#Ning Xie, Hirotaka Hachiya, and Masashi Sugiyama. Artist agent: A reinforcement learning approach to automatic stroke generation in oriental ink painting. In ICML. icml.cc / Omnipress, 2012. URL http://dblp.uni-trier.de/db/conf/icml/icml2012.html#XieHS12.<br />
# Xu-Yao Zhang, Fei Yin, Yan-Ming Zhang, Cheng-Lin Liu, and Yoshua Bengio. Drawing and Recognizing Chinese Characters with Recurrent Neural Network. CoRR, abs/1606.06539, 2016. URL http://arxiv.org/abs/1606.06539.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DETECTING_STATISTICAL_INTERACTIONS_FROM_NEURAL_NETWORK_WEIGHTS&diff=42271DETECTING STATISTICAL INTERACTIONS FROM NEURAL NETWORK WEIGHTS2018-12-05T04:33:06Z<p>A22ravi: /* Highe-order interatcion detection */</p>
<hr />
<div>=Introduction=<br />
<br />
It has been commonly believed that one major advantage of neural networks is their capability of modelling complex statistical interactions between features for automatic feature learning. Statistical interactions capture important information on where features often have joint effects with other features on predicting an outcome. The discovery of interactions is especially useful for scientific discoveries and hypothesis validation. For example, physicists may be interested in understanding what joint factors provide evidence for new elementary particles; doctors may want to know what interactions are accounted for in risk prediction models, to compare against known interactions from existing medical literature.<br />
<br />
With the growth in the computational power available Neural Networks have been able to solve many of the complex tasks in a wide variety of fields. This is mainly due to their ability to model complex and non-linear interactions. Neural networks have traditionally been treated as “black box” models, preventing their adoption in many application domains, such as those where explainability is desirable. It has been noted that complex machine learning models can learn unintended patterns from data, raising significant risks to stakeholders [14]. Therefore, in applications where machine learning models are intended for making critical decisions, such as healthcare or finance, it is paramount to understand how they make predictions [9]. Within several areas, like eg: computation social science, interpretability is of utmost importance. Since we do not understand how a neural network comes to its decision, practitioners in these areas tend to prefer simpler models like linear regression, decision trees, etc. which are much more interpretable. In this paper, we are going to present one way of implementing interpretability in a neural network.<br />
<br />
Existing approaches to interpreting neural networks can be summarized into two types. One type is direct interpretation, which focuses on 1) explaining individual feature importance, for example by computing input gradients [13] and decomposing predictions [8], 2) developing attention-based models, which illustrate where neural networks focus during inference [11], and 3) providing model-specific visualizations, such as feature map and gate activation visualizations [15]. The other type is indirect interpretation, for example post-hoc interpretations of feature importance [12] and knowledge distillation to simpler interpretable models [10].<br />
<br />
In this paper, the authors propose Neural Interaction Detection (NID), which can detect any order or form of statistical interaction captured by the feedforward neural network by examining its weight matrix. This approach is efficient because it avoids searching over an exponential solution space of interaction candidates by making an approximation of hidden unit importance at the first hidden layer via all weights above and doing a 2D traversal of the input weight matrix.<br />
<br />
Note that in this paper, we only consider one specific types of neural network, feedforward neural network. Based on the methodology discussed here, the authors suggest that we can build an interpretation method for other types of networks also.<br />
<br />
=Related Work=<br />
<br />
1. Interaction Detection approaches: <br />
* Conduct individual tests for all features' combination such as ANOVA and Additive Groves. Two-way ANOVA has been a standard method of performing pairwise interaction detection that involves conducting hypothesis tests for each interaction candidate by checking each hypothesis with F-statistics (Wonnacott & Wonnacott, 1972). Additive Groves is another method that conducts individual tests for interactions and hence must face the same computational difficulties; however, it is special because the interactions it detects are not constrained to any functional form.<br />
* Define all interaction forms of interest, then later finds the important ones.<br />
<br />
- The paper's goal is to detect interactions without compromising the functional forms. Our method accomplishes higher-order interaction detection, which has the benefit of avoiding a high false positive or false discovery rate.<br />
<br />
2. Interpretability: A lot of work has also been done in this particular area and it can be divided it the following broad categories:<br />
* Feature Importance through Decomposition: Methods like Input Gradient(Sundararajan et al., 2017) learns the importance of features through a gradient-based approach similar to backpropagation. Works like Li et al(2017), Murdoch(2017) and Murdoch(2018) study interpretability of LSTMs by looking at phrase and word level importance scores. Bach et al. 2015 and Shrikumar et al. 2016 (DeepLift) study pixel importance in CNNs.<br />
* Studying Visualizations in Models - Karpathy et al. (2015) worked with character generating LSTMs and tried to study activation and firing in certain hidden units for meaningful attributes. (Yosinski et al., 2015 studies feature map visualizations, providing a tool for visualizing live activations on each layer of a trained CNN, and another for visualizing "Regularized Optimization".) <br />
* Attention-Based Models: Bahdanau et al. (2014) - These are a different class of models which use attention modules(different architectures) to help focus the neural network to decide the parts of the input that it should look more closely or give more importance to. Looking at the results of these type of model an indirect sense of interpretability can be gauged.<br />
* Sum product networks, Hoifun Poon, Pedro Domingos (2011) It is a new deep architecture that provides clear semantics. In its core, it is a probabilistic model, with two types of nodes: Sum node and Product nodes. The sum nodes are trying to model the mixture of distributions and product node is trying to model joint distributions. It can be trained using gradient descent and other methods as well. The main advantage of the Sum-Product Network is that it has clear semantics, where people can interpret exactly how the network models make decisions. Therefore, it has better interpretability than most of the current deep architectures. <br />
<br />
The approach in this paper is to extract non-additive interactions between variables from the neural network weights.<br />
<br />
=Notations=<br />
Before we dive in to methodology, we are going to define a few notations here. Most of them will be trivial.<br />
<br />
1. Vector: Vectors are defined with bold-lowercases, '''v, w'''<br />
<br />
2. Matrix: Matrice are defined with blod-uppercases, '''V, W'''<br />
<br />
3. Interger Set: For some interger p <math>\in</math> Z, we define [p] := {1,2,3,...,p}<br />
<br />
=Interaction=<br />
First of all, in order to explain the model, we need to be able to explain the interactions and their effects to output. Therefore, we define 'interacion' between variables as below. <br />
<br />
[[File:def_interaction.PNG|900px|center]]<br />
<br />
From the definition above, for a function like, <math>x_1x_2 + sin(x_3 + x_4 + x_5)</math>, we have <math>{[x_1, x_2]}</math> and <math>{[x_3, x_4, x_5]}</math> interactions. And we say that the latter interaction to be 3-way interaction.<br />
<br />
Note that from the definition above, we can naturally deduce that d-way interaction can exist if and only if all of its (d-1) interactions exist. For example, 3-way interaction above shows that we have 2-way interactions <math>{[3,4], [4,5]}</math> and <math>{[3,5]}</math>.<br />
<br />
One thing that we need to keep in mind is that for models like neural network, most of interactions are happening within hidden layers. This means that we needa proper way of measuring interaction strength.<br />
<br />
The key observation is that for any kinds of interaction, at a some hidden unit of some hidden layer, two interacting features the ancestors. In graph-theoretical language, interaction map can be viewed as an associated directed graph and for any interaction <math>\Gamma \in [p]</math>, there exists at least one vertix that has all of features of <math>\Gamma</math> as ancestors. The statement can be rigorized as the following:<br />
<br />
<br />
[[File:prop2.PNG|900px|center]]<br />
<br />
Now, the above mathematical statement gurantees us to measure interaction strengths at ANY hidden layers. For example, if we want to study about interactions at some specific hidden layer, now we now that there exists corresponding vertices between the hidden layer and output layer. Therefore all we need to do is now to find approprite measure which can summarize the information between those two layers.<br />
<br />
Before doing so, let's think about a single-layered neural network. For any one hidden unit, we can have possibly, <math>2^{||W_i,:||}</math>, number of interactions. This means that our search space might be too huge for multi-layered networks. Therefore, we need a some descent way of approximate out search space. Moreover, the authors realized a fast interaction detection by limiting the search complexity of the task by only quantifying interactions created at the first hidden layer. The figure below illustrates an interaction within a fully connected feedforward neural network, where the box contains later layers in the network.<br />
<br />
[[File:network1.PNG|500px|center]]<br />
<br />
==Measuring influence in hidden layers==<br />
As we discussed above, in order to consider interaction between units in any layers, we need to think about their out-going paths. However, we soon encountered the fact that for some fully-connected multi-layer neural network, the search space might be too huge to compare. Therefore, we use information about out-going paths gredient upper bond. To represent the influence of out-going paths at <math>l</math>-hidden layer, we define cumulative impact of weights between output layer and <math>l+1</math>. We define aggregated weights as, <br />
<br />
[[File:def3.PNG|900px|center]]<br />
<br />
<br />
Note that <math>z^{(l)} \in R^{(p_l)}</math> where <math>p_l</math> is the number of hidden units in <math>l</math>-layer.<br />
Moreover, this is the lipschitz constant of gredients. Gredient has been an import variable of measuring influence of features, especially when we consider that input layer's derivative computes the direction normal to decision boundaries.<br />
<br />
==Quantifying influence==<br />
For some <math>i</math> hidden unit at the first hidden layer, which is the closet layer to the input layer, we define the influence strength of some interaction as, <br />
<br />
[[File:measure1.PNG|900px|center]]<br />
<br />
The function <math>\mu</math> will be defined later. Essentially, the formula shows that the strength of influence is defined as the product of the aggregated weight on the first hidden layer and some measure of influence between the first hidden layer and the input layer. <br />
<br />
For the function, <math>\mu</math>, any positive-real valued functions such as max, min and average can be candidates. The effects of those candidates will be tested later.<br />
<br />
Now based on the specifications above, the author suggested the algorithm for searching influential interactions between input layer units as follows:<br />
<br />
It was pointed out that restricting to the first hidden layer might miss some important feature interactions, however, the author state that it is not straightforward how to incorporate the idea of hidden units at intermediate layers to get better interaction detection performance.<br />
[[File:algorithm1.PNG|850px|center]]<br />
<br />
=Cut-off Model=<br />
Now using the greedy algorithm defined above, we can rank the interactions by their strength. However, in order to access true interactions, we are building the cut-off model which is a generalized additive model (GAM) as below,<br />
<br />
<center><math><br />
c_K('''x''') = \sum_{i=1}^{p}g_i(x_i) + \sum_{i=1}^{K}{g_i}^\prime(x_\chi)<br />
</math></center><br />
<br />
From the above model, each of <math>g_i</math> and <math>g_i'</math> are Feed-Forward neural networks. <math>g_i(\cdot)</math> captures the main effects, while <math>g_i'(\cdot)</math> captures the interaction. We are keep adding interactions until the performance reaches plateaus.<br />
<br />
=Experiment=<br />
For the experiment, the authors have compared three neural network model with traditional statistical interaction detecting algorithms. For the nueral network models, first model will be MLP, second model will be MLP-M, which is MLP with additional univariate network at the output. The last one is the cut-off model defined above, which is denoted by MLP-cutoff. In the experiments that the authors performed, all the networks which modelled feature interactions consisted of four hidden layers containing 140, 100, 60, and 20 units respectively. Whereas, all the individual univariate networks contained three hidden layers with each layer containing 10 units. All of these networks used ReLu activation and backpropagation for training. The MLP-M model is graphically represented below.<br />
<br />
[[File:output11.PNG|300px|center]]<br />
<br />
For the experiment, the authors study our interaction detection framework on both simulated and real-world experiments. For simulated experiments, the authors are going to test on 10 synthetic functions as shown in table I.<br />
<br />
[[File:synthetic.PNG|900px|center]]<br />
<br />
The authors use four real-world datasets, of which two are regression datasets, and the other two are binary classification datasets. The datasets are a mixture of common prediction tasks in the cal housing<br />
and bike sharing datasets, a scientific discovery task in the higgs boson dataset, and an example of very-high order interaction detection in the letter dataset.<br />
<br />
And the authors also reported the results of comparisons between the models. As you can see, neural network based models are performing better on average. Compare to the traditional methods like ANOVA, MLP and MLP-M method shows 20% increases in performance.<br />
<br />
[[File:performance_mlpm.PNG|900px|center]]<br />
<br />
<br />
[[File:performance2_mlpm.PNG|900px|center]]<br />
<br />
The above result shows that MLP-M almost perfectly capture the most influential pair-wise interactions.<br />
<br />
=Higher-order interaction detection=<br />
The authors use their greedy interaction ranking algorithm to perform higher-order interactiondetection without an exponential search of interaction candidates.<br />
[[File:higher-order_interaction_detection.png|700px|center]]<br />
<br />
=Limitations=<br />
Even though for the above synthetic experiment MLP methods showed superior performances, the method still have some limitations. For example, fir the function like, <math>x_1x_2 + x_2x_3 + x_1x_3</math>, neural network fails to distinguish between interlinked interactions to single higher order interaction. Moreoever, correlation between features deteriorates the ability of the network to distinguish interactions. However, correlation issues are presented most of interaction detection algorithms. <br />
<br />
In the case of detecting pairwise interactions, the interlinked pairwise interactions are often confused by the algorithm for complex interactions. This means that the higher-order interaction algorithm fails to separate interlinked pairwise interactions encoded in the neural network. Another issue is that it sometimes detects abrupt interactions or misses interactions as a result of correlations between features<br />
<br />
Because this method relies on the neural network fitting the data well, there are some additional concerns. Notably, if the NN is unable to make an appropriate fit (under/overfitting), the resulting interactions will be flawed. This can occur if the datasets that are too small or too noisy, which often occurs in practical settings.<br />
<br />
=Conclusion=<br />
Here we presented the method of detecting interactions using MLP. Compared to other state-of-the-art methods like Additive Groves (AG), the performances are competitive yet computational powers required is far less. Therefore, it is safe to claim that the method will be extremly useful for practitioners with (comparably) less computational powers. Moreover, the NIP algorithm successfully reduced the computation sizes. After all, the most important aspect of this algorithm is that now users of nueral networks can impose interpretability in the model usage, which will change the level of usability to another level for most of practitioners outside of those working in machine learning and deep learning areas.<br />
<br />
For future work, the authors want to detect feature interactions by using the common units in the intermediate hidden layers of feedforward networks, and also want to use such interaction detection to interpret weights in other deep neural networks. Also, it was pointed out that the neural network weights heavily depend on L-1 regularized neural network training, but a group lasso penalty may work better.<br />
<br />
=Critique=<br />
1. Authors need to do large-scale experiments, instead of just conducting experiments on some synthetic dataset with small feature dimensionality, to make their claim stronger.<br />
<br />
2. Although the method proposed in this paper is interesting, the paper would benefit from providing some more explanations to support its idea and fill the possible gaps in its experimental evaluation. In some parts there are repetitive explanations that could be replaced by other essential clarifications.<br />
<br />
3. Greedy algorithm is implemented but nothing is mentioned about the speed of this algorithm which is definitely not fast. So, this has the potential to be a weak point of the study.<br />
<br />
=Reference=<br />
<br />
[1] Jacob Bien, Jonathan Taylor, and Robert Tibshirani. A lasso for hierarchical interactions. Annals of statistics, 41(3):1111, 2013. <br />
<br />
[2] G David Garson. Interpreting neural-network connection weights. AI Expert, 6(4):46–51, 1991.<br />
<br />
[3] Yotam Hechtlinger. Interpretation of prediction models using the input gradient. arXiv preprint arXiv:1611.07634, 2016.<br />
<br />
[4] Shiyu Liang and R Srikant. Why deep neural networks for function approximation? 2016. <br />
<br />
[5] David Rolnick and Max Tegmark. The power of deeper networks for expressing natural functions. International Conference on Learning Representations, 2018. <br />
<br />
[6] Daria Sorokina, Rich Caruana, and Mirek Riedewald. Additive groves of regression trees. Machine Learning: ECML 2007, pp. 323–334, 2007.<br />
<br />
[7] Simon Wood. Generalized additive models: an introduction with R. CRC press, 2006<br />
<br />
[8] Sebastian Bach, Alexander Binder, Gre ́goire Montavon, Frederick Klauschen, Klaus-Robert Mu ̈ller, and Wojciech Samek. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PloS one, 10(7):e0130140, 2015.<br />
<br />
[9] Rich Caruana, Yin Lou, Johannes Gehrke, Paul Koch, Marc Sturm, and Noemie Elhadad. Intel- ligible models for healthcare: Predicting pneumonia risk and hospital 30-day readmission. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1721–1730. ACM, 2015.<br />
<br />
[10] Zhengping Che, Sanjay Purushotham, Robinder Khemani, and Yan Liu. Interpretable deep models for icu outcome prediction. In AMIA Annual Symposium Proceedings, volume 2016, pp. 371. American Medical Informatics Association, 2016.<br />
<br />
[11] Laurent Itti, Christof Koch, and Ernst Niebur. A model of saliency-based visual attention for rapid scene analysis. IEEE Transactions on pattern analysis and machine intelligence, 20(11):1254– 1259, 1998.<br />
<br />
[12] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. Why should i trust you?: Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135–1144. ACM, 2016.<br />
<br />
[13]Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: Vi- sualising image classification models and saliency maps. arXiv preprint arXiv:1312.6034, 2013.<br />
<br />
[14] Kush R Varshney and Homa Alemzadeh. On the safety of machine learning: Cyber-physical sys- tems, decision sciences, and data products. arXiv preprint arXiv:1610.01256, 2016.<br />
<br />
[15] Jason Yosinski, Jeff Clune, Anh Nguyen, Thomas Fuchs, and Hod Lipson. Understanding neural networks through deep visualization. arXiv preprint arXiv:1506.06579, 2015.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=conditional_neural_process&diff=42270conditional neural process2018-12-05T01:58:32Z<p>A22ravi: /* Motivation */</p>
<hr />
<div>== Motivation ==<br />
<br />
Deep neural networks are good at function approximations, yet they are typically trained from scratch for each new function. While Bayesian methods, such as Gaussian Processes (GPs), exploit prior knowledge to quickly infer the shape of a new function at test time. Yet GPs are computationally expensive, and it can be hard to design appropriate priors. Hence the authors propose a family of neural models called, Conditional Neural Processes (CNPs), that combine the benefits of both.<br />
<br />
== Introduction ==<br />
<br />
To train a model effectively, deep neural networks typically require large datasets. To mitigate this data efficiency problem, learning in two phases is one approach: the first phase learns the statistics of a generic domain without committing to a specific learning task; the second phase learns a function for a specific task but does so using only a small number of data points by exploiting the domain-wide statistics already learned. Taking a probabilistic stance and specifying a distribution over functions (stochastic processes) is another approach -- Gaussian Processes being a commonly used example of this. Such Bayesian methods can be computationally expensive. <br />
<br />
The authors of the paper propose a family of models that represent solutions to the supervised problem, and an end-to-end training approach to learning them that combines neural networks with features reminiscent of Gaussian Processes. They call this family of models Conditional Neural Processes (CNPs). CNPs can be trained on very few data points to make accurate predictions, while they also have the capacity to scale to complex functions and large datasets.<br />
<br />
== Model ==<br />
Consider a data set <math display="inline"> \{x_i, y_i\} </math> with evaluations <math display="inline">y_i = f(x_i) </math> for some unknown function <math display="inline">f</math>. Assume <math display="inline">g</math> is an approximating function of f. The aim is to minimize the loss between <math display="inline">f</math> and <math display="inline">g</math> on the entire space <math display="inline">X</math>. In practice, the routine is evaluated on a finite set of observations.<br />
<br />
Let training set be <math display="inline"> O = \{x_i, y_i\}_{i = 0} ^{n-1}</math>, and test set be <math display="inline"> T = \{x_i, y_i\}_{i = n} ^ {n + m - 1} \subset X</math> of unlabelled points.<br />
<br />
P be a probability distribution over functions <math display="inline"> F : X \to Y</math>, formally known as a stochastic process. Thus, P defines a joint distribution over the random variables <math display="inline"> {f(x_i)}_{i = 0} ^{n + m - 1}</math>. Therefore, for <math display="inline"> P(f(x)|O, T)</math>, our task is to predict the output values <math display="inline">f(x_i)</math> for <math display="inline"> x_i \in T</math>, given <math display="inline"> O</math>. <br />
<br />
A good example is given by the authors, consider a random 1-dimensional function <math>f ∼ P</math> defined on the real line (i.e., <math>X := R</math>, <math>Y := R</math>). <math>O</math> would constitute <math>n</math> observations of <math>f</math>’s value <math>y_i</math> at different locations <math>x_i</math> on the real line. Given these observations, we are interested in predicting <math>f</math>’s value at new locations on the real line. <br />
<br />
A common assumption made on P is that all function evaluations of <math display="inline"> f </math> is Gaussian distributed. The random functions class is called Gaussian Processes (GPs). This framework of the stochastic process allows a model to be data efficient, however, it's hard to get appropriate priors and stochastic processes are expensive in computation, scaling poorly with <math>n</math> and <math>m</math>. One of the examples is GPs, which has running time <math>O(n+m)^3</math>.<br />
<br />
[[File:001.jpg|300px|center]]<br />
<br />
== Conditional Neural Process ==<br />
<br />
Conditional Neural Process models directly parametrize conditional stochastic processes without imposing consistency with respect to some prior process. CNP parametrize distributions over <math display="inline">f(T)</math> given a distributed representation of <math display="inline">O</math> of fixed dimensionality. Thus, the mathematical guarantees associated with stochastic processes is traded off for functional flexibility and scalability.<br />
<br />
CNP is a conditional stochastic process <math display="inline">Q_\theta</math> defines distributions over <math display="inline">f(x_i)</math> for <math display="inline">x_i \in T</math>, given a set of observations <math display="inline">O</math>. For stochastic processs, the authors assume that <math display="inline">Q_{\theta}</math> is invariant to permutations, and <math display="inline">Q_\theta(f(T) | O, T)= Q_\theta(f(T') | O, T')=Q_\theta(f(T) | O', T) </math> when <math> O', T'</math> are permutations of <math display="inline">O</math> and <math display="inline">T </math>. In this work, we generally enforce permutation invariance with respect to <math display="inline">T</math> be assuming a factored structure, which is the easiest way to ensure a valid stochastic process. That is, <math display="inline">Q_\theta(f(T) | O, T) = \prod _{x \in T} Q_\theta(f(x) | O, x)</math>. Moreover, this framework can be extended to non-factored distributions.<br />
<br />
In detail, the following architecture is used.<br />
<br />
<math display="inline">r_i = h_\theta(x_i, y_i)</math> &forall; <math display="inline">(x_i, y_i) \in O</math>, where <math display="inline">h_\theta : X \times Y \to \mathbb{R} ^ d</math><br />
<br />
<math display="inline">r = r_i * r_2 * ... * r_n</math>, where <math display="inline">*</math> is a commutative operation that takes elements in <math display="inline">\mathbb{R}^d</math> and maps them into a single element of <math display="inline">\mathbb{R} ^ d</math><br />
<br />
<math display="inline">\Phi_i = g_\theta</math> &forall; <math display="inline">x_i \in T</math>, where <math display="inline">g_\theta : X \times \mathbb{R} ^ d \to \mathbb{R} ^ e</math> and <math display="inline">\Phi_i</math> are parameters for <math display="inline">Q_\theta</math><br />
<br />
Note that this architecture ensures permutation invariance and <math display="inline">O(n + m)</math> scaling for conditional prediction. Also, <math display="inline">r = r_i * r_2 * ... * r_n</math> can be computed in <math display="inline">O(n)</math>, this architecture supports streaming observation with minimal overhead.<br />
<br />
We train <math display="inline">Q_\theta</math> by asking it to predict <math display="inline">O</math> conditioned on a randomly<br />
chosen subset of <math display="inline">O</math>. This gives the model a signal of the uncertainty over the space X inherent in the distribution<br />
P given a set of observations. The authors let <math display="inline"> f \sim P</math>, <math display="inline"> O = \{(x_i, y_i)\}_{i = 0} ^{n-1}</math>, and N ~ uniform[0, 1, ..... ,n-1]. Subset <math display="inline"> O = \{(x_i, y_i)\}_{i = 0} ^{N}</math> that is first N elements of <math display="inline">O</math> is regarded as condition. The negative conditional log probability is given by<br />
\[\mathcal{L}(\theta)=-\mathbb{E}_{f \sim p}[\mathbb{E}_{N}[\log Q_\theta(\{y_i\}_{i = 0} ^{n-1}|O_{N}, \{x_i\}_{i = 0} ^{n-1})]]\]<br />
Thus, the targets it scores <math display="inline">Q_\theta</math> on include both the observed <br />
and unobserved values. In practice, Monte Carlo estimates of the gradient of this loss is taken by sampling <math display="inline">f</math> and <math display="inline">N</math>. <br />
<br />
This approach shifts the burden of imposing prior knowledge from an analytic prior to empirical data. This has the advantage of liberating a practitioner from having to specify an analytic form for the prior, which is ultimately<br />
intended to summarize their empirical experience. Still, we emphasize that the <math display="inline">Q_\theta</math> are not necessarily a consistent set of conditionals for all observation sets, and the training routine does not guarantee that.<br />
<br />
In summary,<br />
<br />
1. A CNP is a conditional distribution over functions<br />
trained to model the empirical conditional distributions<br />
of functions <math display="inline">f \sim P</math>.<br />
<br />
2. A CNP is permutation invariant in <math display="inline">O</math> and <math display="inline">T</math>.<br />
<br />
3. A CNP is scalable, achieving a running time complexity<br />
of <math display="inline">O(n + m)</math> for making <math display="inline">m</math> predictions with <math display="inline">n</math><br />
observations.<br />
<br />
== Related Work ==<br />
<br />
===Gaussian Process Framework===<br />
<br />
A Gaussian Process (GP) is a non-parametric method for regression, used extensively for regression and classification problems in the machine learning community. A GP is defined as a collection of random variables, any finite number of which have a joint Gaussian distribution.<br />
A standard approach is to model data as <math>y = m(X, φ) + \epsilon</math><br />
where <math>m</math> is the mean function with parameter vector <math>φ</math>, and <math>\epsilon</math> represents independent and identically distributed (i.i.d.) Gaussian noise: <math>N\sim (0,\sigma^2)</math><br />
<br />
For more info on Gaussian Process Framework:<br />
[https://arxiv.org/abs/1506.07304 A Gaussian process framework for modeling instrumental systematics: application to transmission spectroscopy]<br />
<br />
Several papers attempt to address various issues with GPs. These include:<br />
* Using sparse GPs to aid in scaling (Snelson & Ghahramani, 2006)<br />
* Using Deep GPs to achieve more expressiveness (Damianou & Lawrence, 2013; Salimbeni & Deisenroth, 2017)<br />
* Using neural networks to learn more expressive kernels (Wilson et al., 2016)<br />
<br />
A Python resource for Gaussian Process Framework implementation: [https://github.com/SheffieldML/GPyimplementation Gaussian Process Framework in Python]<br />
<br />
The goal of this paper is to incorporate ideas from standard neural networks with Gaussian processes in order to overcome drawbacks of both. Bayesian techniques work better with less data, but complex Bayesian networks become intractable on even moderate sized data sizes. NNs on the other hand, cannot make use of prior knowledge and often have to be retrained from scratch. Without sufficient data, they also perform poorly. Combining both frameworks, we get Conditional Neural Processes serves to learn the kernels of the Gaussian Process through neural networks and uses these learned kernels on a framework similar to GPs for prediction.<br />
<br />
===Meta Learning===<br />
<br />
Meta-Learning attempts to allow neural networks to learn more generalizable functions, as opposed to only approximating one function. This can be done by learning deep generative models which can do few-shot estimations of data. This can be implemented with attention mechanisms (Reed et al., 2017) or additional memory units in a VAE model (Bornschein et al., 2017). Another successful latent variable approach is to explicitly condition on some context during inference (J. Rezende et al., 2016). Given the generative nature of these models they are usually applied to image generation tasks, but models that include a conditioning class-variable can be used for classification as well. Recently meta-learning has also been applied to a wide range of tasks like RL (Wang et al., 2016; Finn et al., 2017) or program induction (Devlin et al., 2017).<br />
<br />
Classification is another common task in meta-learning. Few-shot classification algorithms usually rely on some distance metric in feature space to compare target images and the observations (Koch et al., 2015), (Santoro et al., 2016).. Matching networks(Vinyals et al., 2016; Bartunov & Vetrov, 2016) are closely related to CNPs. In their case features of samples are compared with target features using an attention kernel. At a higher level one can interpret this model as a CNP where the aggregator is just the concatenation over all input samples and the decoder <math>g</math> contains an explicitly defined distance kernel. In this sense matching networks are closer to GPs than to CNPs, since they require the specification of a distance kernel that CNPs learn from the data instead. In addition, as MNs carry out all- to-all comparisons they scale with <math> O(n × m) </math>, although they can be modified to have the same complexity of <math>O(n + m)</math> as CNPs (Snell et al., 2017).<br />
<br />
Another field in the meta-learning field is Neural architecture search. It requires the search algorithm to define three things: the search space, search strategy, and performance evaluation strategy. It is one of the most popular trends in the meta-learning field now. The idea is we can define some search space, and let algorithms help us decide what architecture and hyperparameters would be best for a particular task. Also, since evaluating a neural network is expensive(needs train the neural network first), it needs a well designed performance evaluation strategy to lower down the computational cost<br />
<br />
A model that is conceptually very similar to CNPs (and in particular the latent variable version) is the “neural statistician” paper (Edwards & Storkey, 2016) and the related variational homoencoder (Hewitt et al., 2018). As with the<br />
other generative models the neural statistician learns to estimate the density of the observed data but does not allow for targeted sampling at what we have been referring to as input positions <math>x_i</math>. Instead, one can only generate i.i.d. samples from the estimated density. Finally, the latest variant of Conditional Neural Process can also be seen as an approximated amortized version of Bayesian DL(Gal & Ghahramani, 2016; Blundell et al., 2015; Louizos et al., 2017; Louizos & Welling, 2017). For example, Gal & Ghahramani 2016 develop a new theoretical framework casting dropout training in deep neural networks as approximate Bayesian inference in deep Gaussian processes. Their theory extracts information from existing models and gives us tools to model uncertainty.<br />
<br />
== Experimental Result I: Function Regression ==<br />
<br />
Classical 1D regression task that used as a common baseline for GP is the first example. <br />
They generated two different datasets that consisted of functions<br />
generated from a GP with an exponential kernel. In the first dataset they used a kernel with fixed parameters, and in the second dataset, the function switched at some random point. on the real line between two functions, each sampled with<br />
different kernel parameters. At every training step, they sampled a curve from the GP, select<br />
a subset of n points as observations, and a subset of t points as target points. Using the model, the observed points are encoded using a three-layer MLP encoder h with a 128-dimensional output representation. The representations are aggregated into a single representation<br />
<math display="inline">r = \frac{1}{n} \sum r_i</math><br />
, which is concatenated to <math display="inline">x_t</math> and passed to a decoder g consisting of a five layer<br />
MLP. The function outputs a Gaussian mean and variance for the target outputs. The model is trained to maximize the log-likelihood of the target points using the Adam optimizer. <br />
<br />
Two examples of the regression results obtained for each<br />
of the datasets are shown in the following figure.<br />
<br />
[[File:007.jpg|300px|center]]<br />
<br />
They compared the model to the predictions generated by a GP with the correct<br />
hyperparameters, which constitutes an upper bound on our<br />
performance. Although the prediction generated by the GP<br />
is smoother than the CNP's prediction both for the mean<br />
and variance, the model is able to learn to regress from a few<br />
context points for both the fixed kernels and switching kernels.<br />
As the number of context points grows, the accuracy<br />
of the model improves and the approximated uncertainty<br />
of the model decreases. Crucially, we see the model learns<br />
to estimate its own uncertainty given the observations very<br />
accurately. Nonetheless, it provides a good approximation<br />
that increases in accuracy as the number of context points<br />
increases.<br />
Furthermore, the model achieves similarly good performance<br />
on the switching kernel task. This type of regression task<br />
is not trivial for GPs whereas in our case we only have to<br />
change the dataset used for training<br />
<br />
== Experimental Result II: Image Completion for Digits ==<br />
<br />
[[File:002.jpg|600px|center]]<br />
<br />
They also tested CNP on the MNIST dataset and use the test<br />
set to evaluate its performance. As shown in the above figure the<br />
model learns to make good predictions of the underlying<br />
digit even for a small number of context points. Crucially,<br />
when conditioned only on one non-informative context point the model’s prediction corresponds<br />
to the average overall MNIST digits. As the number<br />
of context points increases the predictions become more<br />
similar to the underlying ground truth. This demonstrates<br />
the model’s capacity to extract dataset specific prior knowledge.<br />
It is worth mentioning that even with a complete set<br />
of observations, the model does not achieve pixel-perfect<br />
reconstruction, as we have a bottleneck at the representation<br />
level.<br />
<br />
To generate a coherent sample,<br />
the authors compute the representation r from the observations,<br />
which parametrizes a Gaussian distribution over the latents z.<br />
Then z sampled once and used to generate the predictions<br />
for all targets. To get a different coherent sample they draw a<br />
new sample from the latents z and run the decoder again for<br />
all targets.<br />
<br />
Since this implementation of CNP returns factored outputs,<br />
the best prediction it can produce given limited context<br />
information is to average over all possible predictions that<br />
agree with the context. An alternative to this is to add<br />
latent variables in the model such that they can be sampled<br />
conditioned on the context to produce predictions with high<br />
probability in the data distribution. <br />
<br />
In order to generate a coherent sample,<br />
we compute the representation r from the observations,<br />
which parametrizes a Gaussian distribution over the latents z.<br />
z is then sampled once and used to generate the predictions<br />
for all targets. To get a different coherent sample we draw a<br />
new sample from the latents z and run the decoder again for<br />
all targets.<br />
<br />
<br />
An important aspect of the model is its ability to estimate<br />
the uncertainty of the prediction. As shown in the bottom<br />
row of the above figure, as they added more observations, the variance<br />
shifts from being almost uniformly spread over the digit<br />
positions to being localized around areas that are specific<br />
to the underlying digit, specifically its edges. Being able to<br />
model the uncertainty given some context can be helpful for<br />
many tasks. One example is active exploration, where the<br />
model has a choice over where to observe.<br />
They tested this by<br />
comparing the predictions of CNP when the observations<br />
are chosen according to uncertainty, versus random pixels. This method is a very simple way of doing active<br />
exploration, but it already produces better prediction results<br />
then selecting the conditioning points at random.<br />
<br />
== Experimental Result III: Image Completion for Faces ==<br />
<br />
<br />
[[File:003.jpg|400px|center]]<br />
<br />
<br />
They also applied CNP to CelebA, a dataset of images of<br />
celebrity faces and reported performance obtained on the<br />
test set.<br />
<br />
As shown in the above figure our model is able to capture<br />
the complex shapes and colors of this dataset with predictions<br />
conditioned on less than 10% of the pixels being<br />
already close to the ground truth. As before, given a few contexts<br />
points the model averages over all possible faces, but as<br />
the number of context pairs increases the predictions capture<br />
image-specific details like face orientation and facial<br />
expression. Furthermore, as the number of context points<br />
increases the variance is shifted towards the edges in the<br />
image.<br />
<br />
[[File:004.jpg|400px|center]]<br />
<br />
An important aspect of CNPs demonstrated in the above figure is<br />
it's flexibility not only in the number of observations and<br />
targets it receives but also with regards to their input values.<br />
It is interesting to compare this property to GPs on one hand,<br />
and to trained generative models (van den Oord et al., 2016;<br />
Gregor et al., 2015) on the other hand.<br />
The first type of flexibility can be seen when conditioning on<br />
subsets that the model has not encountered during training.<br />
Consider conditioning the model on one half of the image,<br />
fox example. This forces the model to not only predict the pixel<br />
values according to some stationary smoothness property of<br />
the images, but also according to global spatial properties,<br />
e.g. symmetry and the relative location of different parts of<br />
faces. As seen in the first row of the figure, CNPs are able to<br />
capture those properties. A GP with a stationary kernel cannot<br />
capture this, and in the absence of observations would<br />
revert to its mean (the mean itself can be non-stationary but<br />
usually, this would not be enough to capture the interesting<br />
properties).<br />
<br />
In addition, the model is flexible with regards to the target<br />
input values. This means, e.g., we can query the model<br />
at resolutions it has not seen during training. We take a<br />
model that has only been trained using pixel coordinates of<br />
a specific resolution and predict at test time subpixel values<br />
for targets between the original coordinates. As shown in<br />
Figure 5, with one forward pass we can query the model at<br />
different resolutions. While GPs also exhibit this type of<br />
flexibility, it is not the case for trained generative models,<br />
which can only predict values for the pixel coordinates on<br />
which they were trained. In this sense, CNPs capture the best<br />
of both worlds – it is flexible in regards to the conditioning<br />
and prediction task and has the capacity to extract domain<br />
knowledge from a training set.<br />
<br />
[[File:010.jpg|400px|center]]<br />
<br />
<br />
They compared CNPs quantitatively to two related models:<br />
kNNs and GPs. As shown in the above table CNPs outperform<br />
the latter when a number of context points are small (empirically<br />
when half of the image or less is provided as context).<br />
When the majority of the image is given as context exact<br />
methods like GPs and kNN will perform better. From the table<br />
we can also see that the order in which the context points<br />
are provided is less important for CNPs, since providing the<br />
context points in order from top to bottom still results in<br />
good performance. Both insights point to the fact that CNPs<br />
learn a data-specific ‘prior’ that will generate good samples<br />
even when the number of context points is very small.<br />
<br />
== Experimental Result IV: Classification ==<br />
Finally, they applied the model to one-shot classification using the Omniglot dataset. This dataset consists of 1,623 classes of characters from 50 different alphabets. Each class has only 20 examples and as such this dataset is particularly suitable for few-shot learning algorithms. The authors used 1,200 randomly selected classes as their training set and the remainder as the testing data set.<br />
<br />
Additionally, to apply data augmentation the authors cropped the image from 32 × 32 to 28 × 28, applied small random<br />
translations and rotations to the inputs, and also increased<br />
the number of classes by rotating every character by 90<br />
degrees and defining that to be a new class. They generated<br />
the labels for an N-way classification task by choosing N<br />
random classes at each training step and arbitrarily assigning<br />
the labels <math>0, ..., N − 1</math> to each.<br />
<br />
<br />
[[File:008.jpg|400px|center]]<br />
<br />
Given that the input points are images, they modified the architecture<br />
of the encoder h to include convolution layers as<br />
mentioned in section 2. In addition, they only aggregated over<br />
inputs of the same class by using the information provided<br />
by the input label. The aggregated class-specific representations<br />
are then concatenated to form the final representation.<br />
Given that both the size of the class-specific representations<br />
and the number of classes is constant, the size of the final<br />
representation is still constant and thus the <math>O(n + m)</math><br />
runtime still holds.<br />
The results of the classification are summarized in the following table<br />
CNPs achieve higher accuracy than models that are significantly<br />
more complex (like MANN). While CNPs do not<br />
beat state of the art for one-shot classification our accuracy<br />
values are comparable. Crucially, they reached those values<br />
using a significantly simpler architecture (three convolutional<br />
layers for the encoder and a three-layer MLP for the<br />
decoder) and with a lower runtime of <math>O(n + m)</math> at test time<br />
as opposed to <math>O(nm)</math><br />
<br />
== Conclusion ==<br />
<br />
The paper introduced Conditional Neural Processes,<br />
a model that is both flexible at test time and has the<br />
capacity to extract prior knowledge from training data.<br />
<br />
The authors had demonstrated its ability to perform a variety of tasks<br />
including regression, classification and image completion.<br />
The paper compared CNP's to Gaussian Processes on one hand, and<br />
deep learning methods on the other, and also discussed the<br />
relation to meta-learning and few-shot learning.<br />
It is important to note that the specific CNP implementations<br />
described here are just simple proofs-of-concept and can<br />
be substantially extended, e.g. by including more elaborate<br />
architectures in line with modern deep learning advances.<br />
To summarize, this work can be seen as a step towards learning<br />
high-level abstractions, one of the grand challenges of<br />
contemporary machine learning. Functions learned by most<br />
Conditional Neural Processes<br />
conventional deep learning models are tied to a specific, constrained<br />
statistical context at any stage of training. A trained<br />
CNP is more general, in that it encapsulates the high-level<br />
statistics of a family of functions. As such it constitutes a<br />
high-level abstraction that can be reused for multiple tasks.<br />
In future work, they are going to explore how far these models can<br />
help in tackling the many key machine learning problems<br />
that seem to hinge on abstraction, such as transfer learning,<br />
meta-learning, and data efficiency.<br />
<br />
== Critiques ==<br />
<br />
This paper introduces a method, for reducing the computational complexity of the more famous Gaussian Processes model, but they have mentioned a complexity of O(n + m) which is almost the same order of RBF kernel GP. With respect to performances in a sequence of tasks, the authors have not made metric comparisons to GP methods to prove the superiority of their approach.<br />
<br />
It appears that the proposed model is effective in making accurate predictions using lower quality inputs. For example, a dataset with fewer data points or an image with fewer pixels. However, it is not clear whether the proposed algorithm can be trained with a smaller amount of input data.<br />
<br />
== Other Sources ==<br />
# Code for this model and a simpler explanation can be found at [https://github.com/deepmind/conditional-neural-process]<br />
# A newer version of the model is described in this paper [https://arxiv.org/pdf/1807.01622.pdf]<br />
# A good blog post on neural processes [https://kasparmartens.rbind.io/post/np/]<br />
<br />
== Reference ==<br />
Bartunov, S. and Vetrov, D. P. Fast adaptation in generative<br />
models with generative matching networks. arXiv<br />
preprint arXiv:1612.02192, 2016.<br />
<br />
Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra,<br />
D. Weight uncertainty in neural networks. arXiv preprint<br />
arXiv:1505.05424, 2015.<br />
<br />
Bornschein, J., Mnih, A., Zoran, D., and J. Rezende, D.<br />
Variational memory addressing in generative models. In<br />
Advances in Neural Information Processing Systems, pp.<br />
3923–3932, 2017.<br />
<br />
Damianou, A. and Lawrence, N. Deep gaussian processes.<br />
In Artificial Intelligence and Statistics, pp. 207–215,<br />
2013.<br />
<br />
Devlin, J., Bunel, R. R., Singh, R., Hausknecht, M., and<br />
Kohli, P. Neural program meta-induction. In Advances in<br />
Neural Information Processing Systems, pp. 2077–2085,<br />
2017.<br />
<br />
Edwards, H. and Storkey, A. Towards a neural statistician.<br />
2016.<br />
<br />
Finn, C., Abbeel, P., and Levine, S. Model-agnostic metalearning<br />
for fast adaptation of deep networks. arXiv<br />
preprint arXiv:1703.03400, 2017.<br />
<br />
Gal, Y. and Ghahramani, Z. Dropout as a bayesian approximation:<br />
Representing model uncertainty in deep learning.<br />
In international conference on machine learning, pp.<br />
1050–1059, 2016.<br />
<br />
Garnelo, M., Arulkumaran, K., and Shanahan, M. Towards<br />
deep symbolic reinforcement learning. arXiv preprint<br />
arXiv:1609.05518, 2016.<br />
<br />
Gregor, K., Danihelka, I., Graves, A., Rezende, D. J., and<br />
Wierstra, D. Draw: A recurrent neural network for image<br />
generation. arXiv preprint arXiv:1502.04623, 2015.<br />
<br />
Hewitt, L., Gane, A., Jaakkola, T., and Tenenbaum, J. B. The<br />
variational homoencoder: Learning to infer high-capacity<br />
generative models from few examples. 2018.<br />
<br />
J. Rezende, D., Danihelka, I., Gregor, K., Wierstra, D.,<br />
et al. One-shot generalization in deep generative models.<br />
In International Conference on Machine Learning, pp.<br />
1521–1529, 2016.<br />
<br />
Kingma, D. P. and Ba, J. Adam: A method for stochastic<br />
optimization. arXiv preprint arXiv:1412.6980, 2014.<br />
<br />
Kingma, D. P. and Welling, M. Auto-encoding variational<br />
bayes. arXiv preprint arXiv:1312.6114, 2013.<br />
<br />
Koch, G., Zemel, R., and Salakhutdinov, R. Siamese neural<br />
networks for one-shot image recognition. In ICML Deep<br />
Learning Workshop, volume 2, 2015.<br />
<br />
Lake, B. M., Salakhutdinov, R., and Tenenbaum, J. B.<br />
Human-level concept learning through probabilistic program<br />
induction. Science, 350(6266):1332–1338, 2015.<br />
<br />
Lake, B. M., Ullman, T. D., Tenenbaum, J. B., and Gershman,<br />
S. J. Building machines that learn and think like<br />
people. Behavioral and Brain Sciences, 40, 2017.<br />
<br />
LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P. Gradientbased<br />
learning applied to document recognition. Proceedings<br />
of the IEEE, 86(11):2278–2324, 1998.<br />
<br />
Liu, Z., Luo, P., Wang, X., and Tang, X. Deep learning face<br />
attributes in the wild. In Proceedings of International<br />
Conference on Computer Vision (ICCV), December 2015.<br />
<br />
Louizos, C. and Welling, M. Multiplicative normalizing<br />
flows for variational bayesian neural networks. arXiv<br />
preprint arXiv:1703.01961, 2017.<br />
<br />
Louizos, C., Ullrich, K., and Welling, M. Bayesian compression<br />
for deep learning. In Advances in Neural Information<br />
Processing Systems, pp. 3290–3300, 2017.<br />
<br />
Rasmussen, C. E. and Williams, C. K. Gaussian processes<br />
in machine learning. In Advanced lectures on machine<br />
learning, pp. 63–71. Springer, 2004.<br />
<br />
Reed, S., Chen, Y., Paine, T., Oord, A. v. d., Eslami, S.,<br />
J. Rezende, D., Vinyals, O., and de Freitas, N. Few-shot<br />
autoregressive density estimation: Towards learning to<br />
learn distributions. 2017.<br />
<br />
Rezende, D. J., Mohamed, S., and Wierstra, D. Stochastic<br />
backpropagation and approximate inference in deep generative<br />
models. arXiv preprint arXiv:1401.4082, 2014.<br />
<br />
Salimbeni, H. and Deisenroth, M. Doubly stochastic variational<br />
inference for deep gaussian processes. In Advances<br />
in Neural Information Processing Systems, pp.<br />
4591–4602, 2017.<br />
<br />
Santoro, A., Bartunov, S., Botvinick, M., Wierstra, D., and<br />
Lillicrap, T. One-shot learning with memory-augmented<br />
neural networks. arXiv preprint arXiv:1605.06065, 2016.<br />
<br />
Snell, J., Swersky, K., and Zemel, R. Prototypical networks<br />
for few-shot learning. In Advances in Neural Information<br />
Processing Systems, pp. 4080–4090, 2017.<br />
<br />
Snelson, E. and Ghahramani, Z. Sparse gaussian processes<br />
using pseudo-inputs. In Advances in neural information<br />
processing systems, pp. 1257–1264, 2006.<br />
<br />
van den Oord, A., Kalchbrenner, N., Espeholt, L., Vinyals,<br />
O., Graves, A., et al. Conditional image generation with<br />
pixelcnn decoders. In Advances in Neural Information<br />
Processing Systems, pp. 4790–4798, 2016.<br />
<br />
Vinyals, O., Blundell, C., Lillicrap, T., Wierstra, D., et al.<br />
Matching networks for one shot learning. In Advances in<br />
Neural Information Processing Systems, pp. 3630–3638,<br />
2016.<br />
<br />
Wang, J. X., Kurth-Nelson, Z., Tirumala, D., Soyer, H.,<br />
Leibo, J. Z., Munos, R., Blundell, C., Kumaran, D., and<br />
Botvinick, M. Learning to reinforcement learn. arXiv<br />
preprint arXiv:1611.05763, 2016.<br />
<br />
Wilson, A. G., Hu, Z., Salakhutdinov, R., and Xing, E. P.<br />
Deep kernel learning. In Artificial Intelligence and Statistics,<br />
pp. 370–378, 2016.<br />
<br />
Damianou, A. and Lawrence, N. Deep gaussian processes.<br />
In Artificial Intelligence and Statistics, pp. 207–215,<br />
2013.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=42269Countering Adversarial Images Using Input Transformations2018-12-05T01:31:17Z<p>A22ravi: /* Terminology */</p>
<hr />
<div>The code for this paper is available here[https://github.com/facebookresearch/adversarial_image_defenses]<br />
<br />
==Motivation ==<br />
As the use of machine intelligence has increased, robustness has become a critical feature to guarantee the reliability of deployed machine-learning systems. However, recent research has shown that existing models are not robust to small, adversarially designed perturbations to the input. Adversarial examples are inputs to Machine Learning models so that an attacker has intentionally designed to cause the model to make a mistake. Adversarially perturbed examples have been deployed to attack image classification services (Liu et al., 2016)[11], speech recognition systems (Cisse et al., 2017a)[12], and robot vision (Melis et al., 2017)[13]. The existence of these adversarial examples has motivated proposals for approaches that increase the robustness of learning systems to such examples. In the example below (Goodfellow et. al) [17], a small perturbation is applied to the original image of a panda, changing the prediction to a gibbon.<br />
<br />
[[File:Panda.png|center]]<br />
<br />
==Introduction==<br />
The paper studies strategies that defend against adversarial example attacks on image classification systems by transforming the images before feeding them to a Convolutional Network Classifier. <br />
Generally, defenses against adversarial examples fall into two main categories:<br />
<br />
# Model-Specific – They enforce model properties such as smoothness and invariance via the learning algorithm. <br />
# Model-Agnostic – They try to remove adversarial perturbations from the input. <br />
<br />
Model-specific defense strategies make strong assumptions about expected adversarial attacks. As a result, they violate the Kerckhoffs principle, which states that adversaries can circumvent model-specific defenses by simply changing how an attack is executed. This paper focuses on increasing the effectiveness of model-agnostic defense strategies. Specifically, they investigated the following image transformations as a means for protecting against adversarial images:<br />
<br />
# Image Cropping and Re-scaling (Graese et al, 2016). <br />
# Bit Depth Reduction (Xu et al, 2017) <br />
# JPEG Compression (Dziugaite et al, 2016) <br />
# Total Variance Minimization (Rudin et al, 1992) <br />
# Image Quilting (Efros & Freeman, 2001). <br />
<br />
These image transformations have been studied against Adversarial attacks such as the fast gradient sign method (Goodfelow et. al., 2015), its iterative extension (Kurakin et al., 2016a), Deepfool (Moosavi-Dezfooli et al., 2016), and the Carlini & Wagner (2017) <math>L_2</math>attack. <br />
<br />
The authors in this paper try to focus on increasing the effectiveness of model-agnostic defense strategies through approaches that:<br />
# remove the adversarial perturbations from input images,<br />
# maintain sufficient information in input images to correctly classify them,<br />
# and are still effective in situations where the adversary has information about the defense strategy being used.<br />
<br />
From their experiments, the strongest defenses are based on Total Variance Minimization and Image Quilting. These defenses are non-differentiable and inherently random which makes it difficult for an adversary to get around them.<br />
<br />
==Previous Work==<br />
Recently, a lot of research has focused on countering adversarial threats. Wang et al [4], proposed a new adversary resistant technique that obstructs attackers from constructing impactful adversarial images. This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which augments the training process but not only included adversarial images constructed from their model but also including adversarial images generated from an ensemble of other models. Their method implemented on an Inception V2 classifier finished 1st among 70 submissions of NIPS 2017 competition on Defenses against Adversarial Attacks. Graese, et al. [3], showed how input transformation such as shifting, blurring and noise can render the majority of the adversarial examples as non-adversarial. Xu et al.[5] demonstrated, how feature squeezing methods, such as reducing the color bit depth of each pixel and spatial smoothing, defends against attacks. Dziugaite et al [6], studied the effect of JPG compression on adversarial images. Chen et al. [7] introduce an advanced denoising algorithm with GAN based noise modeling in order to improve the blind denoising performance in low-level vision processing. The GAN is trained to estimate the noise distribution over the input noisy images and to generate noise samples. Although meant for image processing, this method can be generalized to target adversarial examples where the unknown noise generating algorithm can be leveraged.<br />
<br />
==Terminology==<br />
<br />
'''Gray Box Attack''' : Model Architecture and parameters are public.<br />
<br />
'''Black Box Attack''': Consider a weak adversary with access to the DNN output only. The adversary has no knowledge<br />
of the architectural choices made to design the DNN, which include the number, type, and size of layers, nor of<br />
the training data used to learn the DNN’s parameters. Such attacks are referred to as black box, where adversaries need<br />
not know internal details of a system to compromise it [18].<br />
<br />
An interesting and important observation of adversarial examples is that they generally are not model or architecture specific. Adversarial examples generated for one neural network architecture will transfer very well to another architecture. In other words, if you wanted to trick a model you could create your own model and adversarial examples based off of it. Then these same adversarial examples will most probably trick the other model as well. This has huge implications as it means that it is possible to create adversarial examples for a completely black box model where we have no prior knowledge of the internal mechanics. [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]<br />
<br />
'''Non Targeted Adversarial Attack''': The goal of the attack is to modify a source image in a way such that the image will be classified incorrectly by the network.<br />
<br />
This is an example on non-targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:non-targeted O.JPG| 600px|center]]<br />
<br />
'''Targeted Adversarial Attack''': The goal of the attack is to modify a source image in way such that image will be classified as a ''target'' class by the network.<br />
<br />
This is an example on targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:Targeted O.JPG| 600px|center]]<br />
<br />
'''Defense''': A defense is a strategy that aims to make the prediction on an adversarial example <math> h(x') </math> equal to the prediction on the corresponding clean example <math> h(x) </math>.<br />
<br />
== Problem Definition ==<br />
The paper discusses non-targeted adversarial attacks for image recognition systems. Given image space <math>\mathcal{X} = [0,1]^{H \times W \times C}</math>, a source image <math>x \in \mathcal{X}</math>, and a classifier <math>h(.)</math>, a non-targeted adversarial example of <math>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity function <math>d(·, ·)</math> and <math>\rho \geq 0</math>. In the best case scenario, <math>d(·, ·)</math> measures the perceptual difference between the original image <math>x</math> and the perturbed image <math>x'</math>, but usually, Euclidean distance (<math>||x - x'||_2</math>) or the Chebyshov distance (<math>||x - x'||_{\infty}</math>) are used.<br />
<br />
From a set of N clean images <math>[{x_{1}, …, x_{N}}]</math>, an adversarial attack aims to generate <math>[{x'_{1}, …, x'_{N}}]</math> images, such that (<math>x'_{n}</math>) is an adversary of (<math>x_{n}</math>).<br />
<br />
The success rate of an attack is given as: <br />
<br />
<center><math><br />
\frac{1}{N}\sum_{n=1}^{N}I[h(x_n) &ne; h({x_n}^\prime)],<br />
</math></center><br />
<br />
which is the proportions of predictions that were altered by an attack.<br />
<br />
The success rate is generally measured as a function of the magnitude of perturbations performed by the attack. In this paper, L2 perturbations are used and are quantified using the normalized L2-dissimilarity metric:<br />
<math> \frac{1}{N} \sum_{n=1}^N{\frac{\vert \vert x_n - x'_n \vert \vert_2}{\vert \vert x_n \vert \vert_2}} </math><br />
<br />
A strong adversarial attack has a high rate, while its normalized L2-dissimilarity given by the above equation is less.<br />
<br />
In most practical settings, an adversary does not have direct access to the model <math>h(·)</math> and has to do a black-box attack. <br />
<br />
However, prior work has shown successful attacks by transferring adversarial examples generated for a separately-trained model to an unknown target model (Liu et al., 2016), thus allowing efficient black-box attack. <br />
<br />
As a result, the authors investigate both the black-box and a more difficult gray-box attack setting: the adversary has access to the model architecture and the model parameters, but<br />
is unaware of the defence strategy that is being used.<br />
<br />
A defence is an approach that aims make the prediction on an adversarial example <math>h(x')</math> equal to the prediction on the corresponding clean example <math>h(x)</math>. In this study, the authors focus on image transformation defenses <math>g(x)</math> that perform prediction via <math>h(g(x'))</math>. Ideally, <math>g(·)</math> is a complex, non-differentiable, and potentially stochastic function: this makes it difficult for an adversary to attack the prediction model <math>h(g(x))</math> even when the adversary knows both <math>h(·)</math> and <math>g(·)</math>.<br />
<br />
==Adversarial Attacks==<br />
<br />
Although the exact effect that adversarial examples have on the network is unknown, Ian Goodfellow et. al's Deep Learning book states that adversarial examples exploit the linearity of neural networks to perturb the cost function to force incorrect classifications. Images are often high resolution, and thus have thousands of pixels (millions for HD images). An epsilon ball perturbation when dimensionality is in the magnitude of thousands/millions greatly effects the cost function (especially if it increases loss at every pixel). Hence, although the following methods such as FGSM and Iterative FGSM are very straightforward, they greatly influence the network under a white box attack. <br />
<br />
For the experimental purposes, below 4 attacks have been studied in the paper:<br />
<br />
1. '''Fast Gradient Sign Method (FGSM; Goodfellow et al. (2015)) [17]''': Given a source input <math>x</math>, and true label <math>y</math>, and let <math>l(.,.)</math> be the differentiable loss function used to train the classifier <math>h(.)</math>. Then the corresponding adversarial example is given by:<br />
<br />
<math>x' = x + \epsilon \cdot sign(\nabla_x l(x, y))</math><br />
<br />
for some <math>\epsilon \gt 0</math> which controls the perturbation magnitude.<br />
<br />
2. '''Iterative FGSM ((I-FGSM; Kurakin et al. (2016b)) [14]''': iteratively applies the FGSM update, where M is the number of iterations. It is given as:<br />
<br />
<math>x^{(m)} = x^{(m-1)} + \epsilon \cdot sign(\nabla_{x^{m-1}} l(x^{m-1}, y))</math><br />
<br />
where <math>m = 1,...,M; x^{(0)} = x;</math> and <math>x' = x^{(M)}</math>. M is set such that <math>h(x) \neq h(x')</math>.<br />
<br />
Both FGSM and I-FGSM work by minimizing the Chebyshev distance between the inputs and the generated adversarial examples.<br />
<br />
3. '''DeepFool ((Moosavi-Dezfooliet al., 2016) [15]''': projects x onto a linearization of the decision boundary defined by binary classifier h(.) for M iterations. This can be particularly effictive when a network uses ReLU activation functions. It is given as:<br />
<br />
[[File:DeepFool.PNG|400px |]]<br />
<br />
4. '''Carlini-Wagner's L2 attack (CW-L2; Carlini & Wagner (2017)) [16]''': propose an optimization-based attack that combines a differentiable surrogate for the model’s classification accuracy with an L2-penalty term which encourages the adversary image to be close to the original image. Let <math>Z(x)</math> be the operation that computes the logit vector (i.e., the output before the softmax layer) for an input <math>x</math>, and <math>Z(x)_k</math> be the logit value corresponding to class <math>k</math>. The untargeted variant<br />
of CW-L2 finds a solution to the unconstrained optimization problem. It is given as:<br />
<br />
[[File:Carlini.PNG|500px |]]<br />
<br />
As mentioned earlier, the first two attacks minimize the Chebyshev distance whereas the last two attacks minimize the Euclidean distance between the inputs and the adversarial examples.<br />
<br />
All the methods described above maintain <math>x' \in \mathcal{X}</math> by performing value clipping. <br />
<br />
Below figure shows adversarial images and corresponding perturbations at five levels of normalized L2-dissimilarity for all four attacks, mentioned above.<br />
<br />
[[File:Strength.PNG|thumb|center| 600px |Figure 1: Adversarial images and corresponding perturbations at five levels of normalized L2- dissimilarity for all four attacks.]]<br />
<br />
==Defenses==<br />
Defense is a strategy that aims to make the prediction on an adversarial example equal to the prediction on the corresponding clean example, and the particular structure of adversarial perturbations <math> x-x' </math> have been shown in Figure 1.<br />
Five image transformations that alter the structure of these perturbations have been studied:<br />
# Image Cropping and Re-scaling, <br />
# Bit Depth Reduction, <br />
# JPEG Compression, <br />
# Total Variance Minimization, <br />
# Image Quilting.<br />
<br />
'''Image cropping and Rescaling''' has the effect of altering the spatial positioning of the adversarial perturbation. In this study, images are cropped and re-scaled during training time as part of data-augmentation. At test time, the predictions of randomly cropped are averaged.<br />
<br />
'''Bit Depth Reduction (Xu et. al) [5]''' performs a simple type of quantization that can remove small (adversarial) variations in pixel values from an image. Images are reduced to 3 bits in the experiment.<br />
<br />
'''JPEG Compression and Decompression (Dziugaite etal., 2016)''' removes small perturbations by performing simple quantization. The authors use a quality level of 75/100 in their experiments<br />
<br />
'''Total Variance Minimization (Rudin et. al) [9]''' :<br />
This combines pixel dropout with total variance minimization. This approach randomly selects a small set of pixels, and reconstructs the “simplest” image that is consistent with the selected pixels. The reconstructed image does not contain the adversarial perturbations because these perturbations tend to be small and localized.Specifically, we first select a random set of pixels by sampling a Bernoulli random variable <math>X(i; j; k)</math> for each pixel location <math>(i; j; k)</math>;we maintain a pixel when <math>(i; j; k)</math>= 1. Next, we use total variation, minimization to constructs an image z that is similar to the (perturbed) input image x for the selected<br />
set of pixels, whilst also being “simple” in terms of total variation by solving:<br />
<br />
[[File:TV!.png|300px|]] , <br />
<br />
where <math>TV_{p}(z)</math> represents <math>L_{p}</math> total variation of '''z''' :<br />
<br />
[[File:TV2.png|500px|]]<br />
<br />
The total variation (TV) measures the amount of fine-scale variation in the image z, as a result of which TV minimization encourages removal of small (adversarial) perturbations in the image. The objective function is convex in <math>z</math>, which makes solving for z straightforward. In the paper, p = 2 and a special-purpose solver based on the split Bregman method (Goldstein & Osher, 2009) to perform total variance minimization efficiently is employed.<br />
The effectiveness of TV minimization is illustrated by the images in the middle column of the figure below: in particular, note that the adversarial perturbations that were present in the background for the non- transformed image (see bottom-left image) have nearly completely disappeared in the TV-minimized adversarial image (bottom-center image). As expected, TV minimization also changes image structure in non-homogeneous regions of the image, but as these perturbations were not adversarially designed we expect the negative effect of these changes to be limited.<br />
<br />
[[File:tvx.png]]<br />
<br />
The figure above represents an illustration of total variance minimization and image quilting applied to an original and an adversarial image (produced using I-FGSM with ε = 0.03, corresponding to a normalized L2 - dissimilarity of 0.075). From left to right, the columns correspond to (1) no transformation, (2) total variance minimization, and (3) image quilting. From top to bottom, rows correspond to: (1) the original image, (2) the corresponding adversarial image produced by I-FGSM, and (3) the absolute difference between the two images above. Difference images were multiplied by a constant scaling factor to increase visibility.<br />
<br />
<br />
'''Image Quilting (Efros & Freeman, 2001) [8]'''<br />
Image Quilting is a non-parametric technique that synthesizes images by piecing together small patches that are taken from a database of image patches. The algorithm places appropriate patches in the database for a predefined set of grid points and computes minimum graph cuts in all overlapping boundary regions to remove edge artifacts. Image Quilting can be used to remove adversarial perturbations by constructing a patch database that only contains patches from "clean" images ( without adversarial perturbations); the patches used to create the synthesized image are selected by finding the K nearest neighbors ( in pixel space) of the corresponding patch from the adversarial image in the patch database, and picking one of these neighbors uniformly at random. The motivation for this defense is that resulting image only contains pixels that were not modified by the adversary - the database of real patches is unlikely to contain the structures that appear in adversarial images.<br />
<br />
If we take a look at the effect of image quilting in the above figure, although interpretation of these images is more complicated due to the quantization errors that image quilting introduces, we can still observe that the absolute differences between quilted original and the quilted adversarial image appear to be smaller in non-homogeneous regions of the image. Based on this observation the authors suggest that TV minimization and image quilting lead to inherently different defenses.<br />
<br />
=Experiments=<br />
<br />
Five experiments were performed to test the efficacy of defenses. The first four experiments consider gray and black box attacks. The gray-box attack applies defenses on input adversarial images for the convolutional networks. The adversary is able to read model architecture and parameters but not the defense strategy. The black-box attack replaces convolutional network by a trained network with image-transformations. The final experiment compares the authors' defenses with prior work. <br />
<br />
'''Set up:'''<br />
Experiments are performed on the ImageNet image classification dataset. The dataset comprises 1.2 million training images and 50,000 test images that correspond to one of 1000 classes. The adversarial images are produced by attacking a ResNet-50 model, with different kinds of attacks mentioned in Section5. The strength of an adversary is measured in terms of its normalized L2-dissimilarity. To produce the adversarial images, L2 dissimilarity for each of the attack was set as below:<br />
<br />
- FGSM. Increasing the step size <math>\epsilon</math>, increases the normalized L2-dissimilarity.<br />
<br />
- I-FGSM. We fix M=10, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- DeepFool. We fix M=5, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- CW-L2. We fix <math>k</math>=0 and <math>\lambda_{f}</math> =10, and multiply the resulting perturbation <br />
<br />
The hyperparameters of the defenses have been fixed in all the experiments. Specifically the pixel dropout probability was set to <math>p</math>=0.5 and regularization parameter of total variation minimizer <math>\lambda_{TV}</math>=0.03.<br />
<br />
Below figure shows the difference between the set up in different experiments below. The network is either trained on a) regular images or b) transformed images. The different settings are marked by 8.1, 8.2 and 8.3 <br />
[[File:models3.png |center]] <br />
<br />
==GrayBox - Image Transformation at Test Time== <br />
This experiment applies a transformation on adversarial images at test time before feeding them to a ResNet -50 which was trained to classify clean images. Below figure shows the results for five different transformations applied and their corresponding Top-1 accuracy. Few of the interesting observations from the plot are: All of the image transformations partly eliminate the effects of the attack, Crop ensemble gives the best accuracy around 40-60 percent, with an ensemble size of 30. The accuracy of Image Quilting Defense hardly deteriorates as the strength of the adversary increases. However, it does impact accuracy on non-adversarial examples.<br />
<br />
[[File:sFig4.png|center|600px |]]<br />
<br />
==BlackBox - Image Transformation at Training and Test Time==<br />
ResNet-50 model was trained on transformed ImageNet Training images. Before feeding the images to the network for training, standard data augmentation (from He et al) along with bit depth reduction, JPEG Compression, TV Minimization, or Image Quilting were applied on the images. The classification accuracy on the same adversarial images as in the previous case is shown Figure below. (Adversary cannot get this trained model to generate new images - Hence this is assumed as a Black Box setting!). Below figure concludes that training Convolutional Neural Networks on images that are transformed in the same way at test time, dramatically improves the effectiveness of all transformation defenses. Nearly 80 -90 % of the attacks are defended successfully, even when the L2- dissimilarity is high.<br />
<br />
<br />
[[File:sFig5.png|center|600px |]]<br />
<br />
<br />
==Blackbox - Ensembling==<br />
Four networks ResNet-50, ResNet-10, DenseNet-169, and Inception-v4 along with an ensemble of defenses were studied, as shown in Table 1. The adversarial images are produced by attacking a ResNet-50 model. The results in the table conclude that Inception-v4 performs best. This could be due to that network having a higher accuracy even in non-adversarial settings. The best ensemble of defenses achieves an accuracy of about 71% against all the other attacks. The attacks deteriorate the accuracy of the best defenses (a combination of cropping, TVM, image quilting, and model transfer) by at most 6%. Gains of 1-2% in classification accuracy could be found from ensembling different defenses, while gains of 2-3% were found from transferring attacks to different network architectures.<br />
<br />
<br />
[[File:sTab1.png|600px|thumb|center|Table 1. Top-1 classification accuracy of ensemble and model transfer defenses (columns) against four black-box attacks (rows). The four networks we use to classify images are ResNet-50 (RN50), ResNet-101 (RN101), DenseNet-169 (DN169), and Inception-v4 (Iv4). Adversarial images are generated by running attacks against the ResNet-50 model, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. Higher is better. The best defense against each attack is typeset in boldface.]]<br />
<br />
==GrayBox - Image Transformation at Training and Test Time ==<br />
In this experiment, the adversary has access to the network and the related parameters (but does not have access to the input transformations applied at test time). From the network trained in-(BlackBox: Image Transformation at Training and Test Time), novel adversarial images were generated by the four attack methods. The results show that Bit-Depth Reduction and JPEG Compression are weak defenses in such a gray box setting. In contrast, image cropping, rescaling, variation minimization, and image quilting are more robust against adversarial images in this setting.<br />
The results for this experiment are shown in below figure. Networks using these defenses classify up to 50 % of images correctly.<br />
<br />
[[File:sFig6.png|center| 600px |]]<br />
<br />
==Comparison With Ensemble Adversarial Training==<br />
The results of the experiment are compared with the state of the art ensemble adversarial training approach proposed by Tramer et al. [2]. Ensemble Training fits the parameters of a Convolutional Neural Network on adversarial examples that were generated to attack an ensemble of pre-trained models. The model release by Tramer et al [2]: an Inception-Resnet-v2, trained on adversarial examples generated by FGSM against Inception-Resnet-v2 and Inception-v3 models. The authors compared their ResNet-50 models with image cropping, total variance minimization and image quilting defenses. Two assumption differences need to be noticed. Their defenses assume the input transformation is unknown to the adversary and no prior knowledge of the attacks is being used. The results of ensemble training and the pre-processing techniques mentioned in this paper are shown in Table 2. The results show that ensemble adversarial training works better on FGSM attacks (which it uses at training time), but is outperformed by each of the transformation-based defenses all other attacks.<br />
<br />
<br />
<br />
[[File:sTab2.png|600px|thumb|center|Table 2. Top-1 classification accuracy on images perturbed using attacks against ResNet-50 models trained on input-transformed images and an Inception-v4 model trained using ensemble adversarial. Adversarial images are generated by running attacks against the models, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. The best defense against each attack is typeset in boldface.]]<br />
<br />
=Discussion/Conclusions=<br />
The paper proposed reasonable approaches to countering adversarial images. The authors evaluated Total Variance Minimization and Image Quilting and compared it with already proposed ideas like Image Cropping - Rescaling, Bit Depth Reduction, JPEG Compression, and Decompression on the challenging ImageNet dataset.<br />
Previous work by Wang et al. [10] shows that a strong input defense should be nondifferentiable and randomized. Two of the defenses - namely Total Variation Minimization and Image Quilting, both possess this property. However, it may still be possible to train a network to perhaps act as an approximation to the non-differentiable transformation. <br />
<br />
Image quilting involves a discrete variable that conducts the selection of a patch from the database, which is a non-differentiable operation.<br />
Additionally, total variation minimization randomly conducts pixels selection from the pixels it uses to measure reconstruction<br />
error during creation of the de-noised image. Image quilting conducts a random selection of a particular K<br />
nearest neighbor uniformly but in a random manner. This inherent randomness makes it difficult to attack the model. <br />
<br />
Future work suggests applying the same techniques to other domains such as speech recognition and image segmentation. For example, in speech recognition, total variance minimization can be used to remove perturbations from waveforms and "spectrogram quilting" techniques that reconstruct a spectrogram could be developed. The proposed input-transformation defenses can also be combined with ensemble adversarial training by Tramèr et al.[2] to study new attack methods.<br />
<br />
=Critiques=<br />
1. The terminology of Black Box, White Box, and Grey Box attack is not exactly given and clear.<br />
<br />
2. White Box attacks could have been considered where the adversary has a full access to the model as well as the pre-processing techniques.<br />
<br />
3. Though the authors did a considerable work in showing the effect of four attacks on ImageNet database, much stronger attacks (Madry et al) [7], could have been evaluated.<br />
<br />
4. Authors claim that the success rate is generally measured as a function of the magnitude of perturbations, performed by the attack using the L2- dissimilarity, but the claim is not supported by any references. None of the previous work has used these metrics.<br />
<br />
5. ([https://openreview.net/forum?id=SyJ7ClWCb])In the new draft of the paper, the authors add the sentence "our defenses assume that part of the defense strategy (viz., the input transformation) is unknown to the adversary".<br />
<br />
This is a completely unreasonable assumption. Any algorithm which hopes to be secure must allow the adversary to, at the very least, understand what the defense is that's being used. Consider a world where the defense here is implemented in practice: any attacker in the world could just go look up the paper, read the description of the algorithm, and know how it works.<br />
<br />
=References=<br />
<br />
1. Chuan Guo , Mayank Rana & Moustapha Ciss´e & Laurens van der Maaten , Countering Adversarial Images Using Input Transformations<br />
<br />
2. Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, Patrick McDaniel, Ensemble Adversarial Training: Attacks and defenses.<br />
<br />
3. Abigail Graese, Andras Rozsa, and Terrance E. Boult. Assessing threat of adversarial examples of deep neural networks. CoRR, abs/1610.04256, 2016. <br />
<br />
4. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Adversary resistant deep neural networks with an application to malware detection. CoRR, abs/1610.01239, 2016a.<br />
<br />
5. Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. CoRR, abs/1704.01155, 2017. <br />
<br />
6. Gintare Karolina Dziugaite, Zoubin Ghahramani, and Daniel Roy. A study of the effect of JPG compression on adversarial images. CoRR, abs/1608.00853, 2016.<br />
<br />
7. Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu .Towards Deep Learning Models Resistant to Adversarial Attacks, arXiv:1706.06083v3<br />
<br />
8. Alexei Efros and William Freeman. Image quilting for texture synthesis and transfer. In Proc. SIGGRAPH, pp. 341–346, 2001.<br />
<br />
9. Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.<br />
<br />
10. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Learning adversary-resistant deep neural networks. CoRR, abs/1612.01401, 2016b.<br />
<br />
11. Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. CoRR, abs/1611.02770, 2016.<br />
<br />
12. Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. CoRR, abs/1707.05373, 2017 <br />
<br />
13. Marco Melis, Ambra Demontis, Battista Biggio, Gavin Brown, Giorgio Fumera, and Fabio Roli. Is deep learning safe for robot vision? adversarial examples against the icub humanoid. CoRR,abs/1708.06939, 2017.<br />
<br />
14. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. Adversarial examples in the physical world. CoRR, abs/1607.02533, 2016b.<br />
<br />
15. Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: A simple and accurate method to fool deep neural networks. In Proc. CVPR, pp. 2574–2582, 2016.<br />
<br />
16. Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy, pp. 39–57, 2017.<br />
<br />
17. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In Proc. ICLR, 2015.<br />
<br />
18. Nicolas Papernot, Patrick McDaniel, Ian Goodfellow, Somesh Jha, Z Berkay Celik, and Ananthram Swami. Practical black-box attacks against machine learning. In ACM Asia Conference on Computer and Communications Security, 2017.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=42268Countering Adversarial Images Using Input Transformations2018-12-05T01:28:03Z<p>A22ravi: /* Terminology */</p>
<hr />
<div>The code for this paper is available here[https://github.com/facebookresearch/adversarial_image_defenses]<br />
<br />
==Motivation ==<br />
As the use of machine intelligence has increased, robustness has become a critical feature to guarantee the reliability of deployed machine-learning systems. However, recent research has shown that existing models are not robust to small, adversarially designed perturbations to the input. Adversarial examples are inputs to Machine Learning models so that an attacker has intentionally designed to cause the model to make a mistake. Adversarially perturbed examples have been deployed to attack image classification services (Liu et al., 2016)[11], speech recognition systems (Cisse et al., 2017a)[12], and robot vision (Melis et al., 2017)[13]. The existence of these adversarial examples has motivated proposals for approaches that increase the robustness of learning systems to such examples. In the example below (Goodfellow et. al) [17], a small perturbation is applied to the original image of a panda, changing the prediction to a gibbon.<br />
<br />
[[File:Panda.png|center]]<br />
<br />
==Introduction==<br />
The paper studies strategies that defend against adversarial example attacks on image classification systems by transforming the images before feeding them to a Convolutional Network Classifier. <br />
Generally, defenses against adversarial examples fall into two main categories:<br />
<br />
# Model-Specific – They enforce model properties such as smoothness and invariance via the learning algorithm. <br />
# Model-Agnostic – They try to remove adversarial perturbations from the input. <br />
<br />
Model-specific defense strategies make strong assumptions about expected adversarial attacks. As a result, they violate the Kerckhoffs principle, which states that adversaries can circumvent model-specific defenses by simply changing how an attack is executed. This paper focuses on increasing the effectiveness of model-agnostic defense strategies. Specifically, they investigated the following image transformations as a means for protecting against adversarial images:<br />
<br />
# Image Cropping and Re-scaling (Graese et al, 2016). <br />
# Bit Depth Reduction (Xu et al, 2017) <br />
# JPEG Compression (Dziugaite et al, 2016) <br />
# Total Variance Minimization (Rudin et al, 1992) <br />
# Image Quilting (Efros & Freeman, 2001). <br />
<br />
These image transformations have been studied against Adversarial attacks such as the fast gradient sign method (Goodfelow et. al., 2015), its iterative extension (Kurakin et al., 2016a), Deepfool (Moosavi-Dezfooli et al., 2016), and the Carlini & Wagner (2017) <math>L_2</math>attack. <br />
<br />
The authors in this paper try to focus on increasing the effectiveness of model-agnostic defense strategies through approaches that:<br />
# remove the adversarial perturbations from input images,<br />
# maintain sufficient information in input images to correctly classify them,<br />
# and are still effective in situations where the adversary has information about the defense strategy being used.<br />
<br />
From their experiments, the strongest defenses are based on Total Variance Minimization and Image Quilting. These defenses are non-differentiable and inherently random which makes it difficult for an adversary to get around them.<br />
<br />
==Previous Work==<br />
Recently, a lot of research has focused on countering adversarial threats. Wang et al [4], proposed a new adversary resistant technique that obstructs attackers from constructing impactful adversarial images. This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which augments the training process but not only included adversarial images constructed from their model but also including adversarial images generated from an ensemble of other models. Their method implemented on an Inception V2 classifier finished 1st among 70 submissions of NIPS 2017 competition on Defenses against Adversarial Attacks. Graese, et al. [3], showed how input transformation such as shifting, blurring and noise can render the majority of the adversarial examples as non-adversarial. Xu et al.[5] demonstrated, how feature squeezing methods, such as reducing the color bit depth of each pixel and spatial smoothing, defends against attacks. Dziugaite et al [6], studied the effect of JPG compression on adversarial images. Chen et al. [7] introduce an advanced denoising algorithm with GAN based noise modeling in order to improve the blind denoising performance in low-level vision processing. The GAN is trained to estimate the noise distribution over the input noisy images and to generate noise samples. Although meant for image processing, this method can be generalized to target adversarial examples where the unknown noise generating algorithm can be leveraged.<br />
<br />
==Terminology==<br />
<br />
'''Gray Box Attack''' : Model Architecture and parameters are public.<br />
<br />
'''Black Box Attack''': Consider a weak adversary with access to the DNN output only. The adversary has no knowledge<br />
of the architectural choices made to design the DNN, which include the number, type, and size of layers, nor of<br />
the training data used to learn the DNN’s parameters. Such attacks are referred to as black box, where adversaries need<br />
not know internal details of a system to compromise it [18].<br />
<br />
An interesting and important observation of adversarial examples is that they generally are not model or architecture specific. Adversarial examples generated for one neural network architecture will transfer very well to another architecture. In other words, if you wanted to trick a model you could create your own model and adversarial examples based off of it. Then these same adversarial examples will most probably trick the other model as well. This has huge implications as it means that it is possible to create adversarial examples for a completely black box model where we have no prior knowledge of the internal mechanics. [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]<br />
<br />
'''Non Targeted Adversarial Attack''': The goal of the attack is to modify a source image in a way such that the image will be classified incorrectly by the network.<br />
<br />
This is an example on non-targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:non-targeted O.JPG| 600px|center]]<br />
<br />
'''Targeted Adversarial Attack''': The goal of the attack is to modify a source image in way such that image will be classified as a ''target'' class by the network.<br />
<br />
This is an example on targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:Targeted O.JPG| 600px|center]]<br />
<br />
'''Defense''': A defense is a strategy that aims make the prediction on an adversarial example h(x') equal to the prediction on the corresponding clean example h(x).<br />
<br />
== Problem Definition ==<br />
The paper discusses non-targeted adversarial attacks for image recognition systems. Given image space <math>\mathcal{X} = [0,1]^{H \times W \times C}</math>, a source image <math>x \in \mathcal{X}</math>, and a classifier <math>h(.)</math>, a non-targeted adversarial example of <math>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity function <math>d(·, ·)</math> and <math>\rho \geq 0</math>. In the best case scenario, <math>d(·, ·)</math> measures the perceptual difference between the original image <math>x</math> and the perturbed image <math>x'</math>, but usually, Euclidean distance (<math>||x - x'||_2</math>) or the Chebyshov distance (<math>||x - x'||_{\infty}</math>) are used.<br />
<br />
From a set of N clean images <math>[{x_{1}, …, x_{N}}]</math>, an adversarial attack aims to generate <math>[{x'_{1}, …, x'_{N}}]</math> images, such that (<math>x'_{n}</math>) is an adversary of (<math>x_{n}</math>).<br />
<br />
The success rate of an attack is given as: <br />
<br />
<center><math><br />
\frac{1}{N}\sum_{n=1}^{N}I[h(x_n) &ne; h({x_n}^\prime)],<br />
</math></center><br />
<br />
which is the proportions of predictions that were altered by an attack.<br />
<br />
The success rate is generally measured as a function of the magnitude of perturbations performed by the attack. In this paper, L2 perturbations are used and are quantified using the normalized L2-dissimilarity metric:<br />
<math> \frac{1}{N} \sum_{n=1}^N{\frac{\vert \vert x_n - x'_n \vert \vert_2}{\vert \vert x_n \vert \vert_2}} </math><br />
<br />
A strong adversarial attack has a high rate, while its normalized L2-dissimilarity given by the above equation is less.<br />
<br />
In most practical settings, an adversary does not have direct access to the model <math>h(·)</math> and has to do a black-box attack. <br />
<br />
However, prior work has shown successful attacks by transferring adversarial examples generated for a separately-trained model to an unknown target model (Liu et al., 2016), thus allowing efficient black-box attack. <br />
<br />
As a result, the authors investigate both the black-box and a more difficult gray-box attack setting: the adversary has access to the model architecture and the model parameters, but<br />
is unaware of the defence strategy that is being used.<br />
<br />
A defence is an approach that aims make the prediction on an adversarial example <math>h(x')</math> equal to the prediction on the corresponding clean example <math>h(x)</math>. In this study, the authors focus on image transformation defenses <math>g(x)</math> that perform prediction via <math>h(g(x'))</math>. Ideally, <math>g(·)</math> is a complex, non-differentiable, and potentially stochastic function: this makes it difficult for an adversary to attack the prediction model <math>h(g(x))</math> even when the adversary knows both <math>h(·)</math> and <math>g(·)</math>.<br />
<br />
==Adversarial Attacks==<br />
<br />
Although the exact effect that adversarial examples have on the network is unknown, Ian Goodfellow et. al's Deep Learning book states that adversarial examples exploit the linearity of neural networks to perturb the cost function to force incorrect classifications. Images are often high resolution, and thus have thousands of pixels (millions for HD images). An epsilon ball perturbation when dimensionality is in the magnitude of thousands/millions greatly effects the cost function (especially if it increases loss at every pixel). Hence, although the following methods such as FGSM and Iterative FGSM are very straightforward, they greatly influence the network under a white box attack. <br />
<br />
For the experimental purposes, below 4 attacks have been studied in the paper:<br />
<br />
1. '''Fast Gradient Sign Method (FGSM; Goodfellow et al. (2015)) [17]''': Given a source input <math>x</math>, and true label <math>y</math>, and let <math>l(.,.)</math> be the differentiable loss function used to train the classifier <math>h(.)</math>. Then the corresponding adversarial example is given by:<br />
<br />
<math>x' = x + \epsilon \cdot sign(\nabla_x l(x, y))</math><br />
<br />
for some <math>\epsilon \gt 0</math> which controls the perturbation magnitude.<br />
<br />
2. '''Iterative FGSM ((I-FGSM; Kurakin et al. (2016b)) [14]''': iteratively applies the FGSM update, where M is the number of iterations. It is given as:<br />
<br />
<math>x^{(m)} = x^{(m-1)} + \epsilon \cdot sign(\nabla_{x^{m-1}} l(x^{m-1}, y))</math><br />
<br />
where <math>m = 1,...,M; x^{(0)} = x;</math> and <math>x' = x^{(M)}</math>. M is set such that <math>h(x) \neq h(x')</math>.<br />
<br />
Both FGSM and I-FGSM work by minimizing the Chebyshev distance between the inputs and the generated adversarial examples.<br />
<br />
3. '''DeepFool ((Moosavi-Dezfooliet al., 2016) [15]''': projects x onto a linearization of the decision boundary defined by binary classifier h(.) for M iterations. This can be particularly effictive when a network uses ReLU activation functions. It is given as:<br />
<br />
[[File:DeepFool.PNG|400px |]]<br />
<br />
4. '''Carlini-Wagner's L2 attack (CW-L2; Carlini & Wagner (2017)) [16]''': propose an optimization-based attack that combines a differentiable surrogate for the model’s classification accuracy with an L2-penalty term which encourages the adversary image to be close to the original image. Let <math>Z(x)</math> be the operation that computes the logit vector (i.e., the output before the softmax layer) for an input <math>x</math>, and <math>Z(x)_k</math> be the logit value corresponding to class <math>k</math>. The untargeted variant<br />
of CW-L2 finds a solution to the unconstrained optimization problem. It is given as:<br />
<br />
[[File:Carlini.PNG|500px |]]<br />
<br />
As mentioned earlier, the first two attacks minimize the Chebyshev distance whereas the last two attacks minimize the Euclidean distance between the inputs and the adversarial examples.<br />
<br />
All the methods described above maintain <math>x' \in \mathcal{X}</math> by performing value clipping. <br />
<br />
Below figure shows adversarial images and corresponding perturbations at five levels of normalized L2-dissimilarity for all four attacks, mentioned above.<br />
<br />
[[File:Strength.PNG|thumb|center| 600px |Figure 1: Adversarial images and corresponding perturbations at five levels of normalized L2- dissimilarity for all four attacks.]]<br />
<br />
==Defenses==<br />
Defense is a strategy that aims to make the prediction on an adversarial example equal to the prediction on the corresponding clean example, and the particular structure of adversarial perturbations <math> x-x' </math> have been shown in Figure 1.<br />
Five image transformations that alter the structure of these perturbations have been studied:<br />
# Image Cropping and Re-scaling, <br />
# Bit Depth Reduction, <br />
# JPEG Compression, <br />
# Total Variance Minimization, <br />
# Image Quilting.<br />
<br />
'''Image cropping and Rescaling''' has the effect of altering the spatial positioning of the adversarial perturbation. In this study, images are cropped and re-scaled during training time as part of data-augmentation. At test time, the predictions of randomly cropped are averaged.<br />
<br />
'''Bit Depth Reduction (Xu et. al) [5]''' performs a simple type of quantization that can remove small (adversarial) variations in pixel values from an image. Images are reduced to 3 bits in the experiment.<br />
<br />
'''JPEG Compression and Decompression (Dziugaite etal., 2016)''' removes small perturbations by performing simple quantization. The authors use a quality level of 75/100 in their experiments<br />
<br />
'''Total Variance Minimization (Rudin et. al) [9]''' :<br />
This combines pixel dropout with total variance minimization. This approach randomly selects a small set of pixels, and reconstructs the “simplest” image that is consistent with the selected pixels. The reconstructed image does not contain the adversarial perturbations because these perturbations tend to be small and localized.Specifically, we first select a random set of pixels by sampling a Bernoulli random variable <math>X(i; j; k)</math> for each pixel location <math>(i; j; k)</math>;we maintain a pixel when <math>(i; j; k)</math>= 1. Next, we use total variation, minimization to constructs an image z that is similar to the (perturbed) input image x for the selected<br />
set of pixels, whilst also being “simple” in terms of total variation by solving:<br />
<br />
[[File:TV!.png|300px|]] , <br />
<br />
where <math>TV_{p}(z)</math> represents <math>L_{p}</math> total variation of '''z''' :<br />
<br />
[[File:TV2.png|500px|]]<br />
<br />
The total variation (TV) measures the amount of fine-scale variation in the image z, as a result of which TV minimization encourages removal of small (adversarial) perturbations in the image. The objective function is convex in <math>z</math>, which makes solving for z straightforward. In the paper, p = 2 and a special-purpose solver based on the split Bregman method (Goldstein & Osher, 2009) to perform total variance minimization efficiently is employed.<br />
The effectiveness of TV minimization is illustrated by the images in the middle column of the figure below: in particular, note that the adversarial perturbations that were present in the background for the non- transformed image (see bottom-left image) have nearly completely disappeared in the TV-minimized adversarial image (bottom-center image). As expected, TV minimization also changes image structure in non-homogeneous regions of the image, but as these perturbations were not adversarially designed we expect the negative effect of these changes to be limited.<br />
<br />
[[File:tvx.png]]<br />
<br />
The figure above represents an illustration of total variance minimization and image quilting applied to an original and an adversarial image (produced using I-FGSM with ε = 0.03, corresponding to a normalized L2 - dissimilarity of 0.075). From left to right, the columns correspond to (1) no transformation, (2) total variance minimization, and (3) image quilting. From top to bottom, rows correspond to: (1) the original image, (2) the corresponding adversarial image produced by I-FGSM, and (3) the absolute difference between the two images above. Difference images were multiplied by a constant scaling factor to increase visibility.<br />
<br />
<br />
'''Image Quilting (Efros & Freeman, 2001) [8]'''<br />
Image Quilting is a non-parametric technique that synthesizes images by piecing together small patches that are taken from a database of image patches. The algorithm places appropriate patches in the database for a predefined set of grid points and computes minimum graph cuts in all overlapping boundary regions to remove edge artifacts. Image Quilting can be used to remove adversarial perturbations by constructing a patch database that only contains patches from "clean" images ( without adversarial perturbations); the patches used to create the synthesized image are selected by finding the K nearest neighbors ( in pixel space) of the corresponding patch from the adversarial image in the patch database, and picking one of these neighbors uniformly at random. The motivation for this defense is that resulting image only contains pixels that were not modified by the adversary - the database of real patches is unlikely to contain the structures that appear in adversarial images.<br />
<br />
If we take a look at the effect of image quilting in the above figure, although interpretation of these images is more complicated due to the quantization errors that image quilting introduces, we can still observe that the absolute differences between quilted original and the quilted adversarial image appear to be smaller in non-homogeneous regions of the image. Based on this observation the authors suggest that TV minimization and image quilting lead to inherently different defenses.<br />
<br />
=Experiments=<br />
<br />
Five experiments were performed to test the efficacy of defenses. The first four experiments consider gray and black box attacks. The gray-box attack applies defenses on input adversarial images for the convolutional networks. The adversary is able to read model architecture and parameters but not the defense strategy. The black-box attack replaces convolutional network by a trained network with image-transformations. The final experiment compares the authors' defenses with prior work. <br />
<br />
'''Set up:'''<br />
Experiments are performed on the ImageNet image classification dataset. The dataset comprises 1.2 million training images and 50,000 test images that correspond to one of 1000 classes. The adversarial images are produced by attacking a ResNet-50 model, with different kinds of attacks mentioned in Section5. The strength of an adversary is measured in terms of its normalized L2-dissimilarity. To produce the adversarial images, L2 dissimilarity for each of the attack was set as below:<br />
<br />
- FGSM. Increasing the step size <math>\epsilon</math>, increases the normalized L2-dissimilarity.<br />
<br />
- I-FGSM. We fix M=10, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- DeepFool. We fix M=5, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- CW-L2. We fix <math>k</math>=0 and <math>\lambda_{f}</math> =10, and multiply the resulting perturbation <br />
<br />
The hyperparameters of the defenses have been fixed in all the experiments. Specifically the pixel dropout probability was set to <math>p</math>=0.5 and regularization parameter of total variation minimizer <math>\lambda_{TV}</math>=0.03.<br />
<br />
Below figure shows the difference between the set up in different experiments below. The network is either trained on a) regular images or b) transformed images. The different settings are marked by 8.1, 8.2 and 8.3 <br />
[[File:models3.png |center]] <br />
<br />
==GrayBox - Image Transformation at Test Time== <br />
This experiment applies a transformation on adversarial images at test time before feeding them to a ResNet -50 which was trained to classify clean images. Below figure shows the results for five different transformations applied and their corresponding Top-1 accuracy. Few of the interesting observations from the plot are: All of the image transformations partly eliminate the effects of the attack, Crop ensemble gives the best accuracy around 40-60 percent, with an ensemble size of 30. The accuracy of Image Quilting Defense hardly deteriorates as the strength of the adversary increases. However, it does impact accuracy on non-adversarial examples.<br />
<br />
[[File:sFig4.png|center|600px |]]<br />
<br />
==BlackBox - Image Transformation at Training and Test Time==<br />
ResNet-50 model was trained on transformed ImageNet Training images. Before feeding the images to the network for training, standard data augmentation (from He et al) along with bit depth reduction, JPEG Compression, TV Minimization, or Image Quilting were applied on the images. The classification accuracy on the same adversarial images as in the previous case is shown Figure below. (Adversary cannot get this trained model to generate new images - Hence this is assumed as a Black Box setting!). Below figure concludes that training Convolutional Neural Networks on images that are transformed in the same way at test time, dramatically improves the effectiveness of all transformation defenses. Nearly 80 -90 % of the attacks are defended successfully, even when the L2- dissimilarity is high.<br />
<br />
<br />
[[File:sFig5.png|center|600px |]]<br />
<br />
<br />
==Blackbox - Ensembling==<br />
Four networks ResNet-50, ResNet-10, DenseNet-169, and Inception-v4 along with an ensemble of defenses were studied, as shown in Table 1. The adversarial images are produced by attacking a ResNet-50 model. The results in the table conclude that Inception-v4 performs best. This could be due to that network having a higher accuracy even in non-adversarial settings. The best ensemble of defenses achieves an accuracy of about 71% against all the other attacks. The attacks deteriorate the accuracy of the best defenses (a combination of cropping, TVM, image quilting, and model transfer) by at most 6%. Gains of 1-2% in classification accuracy could be found from ensembling different defenses, while gains of 2-3% were found from transferring attacks to different network architectures.<br />
<br />
<br />
[[File:sTab1.png|600px|thumb|center|Table 1. Top-1 classification accuracy of ensemble and model transfer defenses (columns) against four black-box attacks (rows). The four networks we use to classify images are ResNet-50 (RN50), ResNet-101 (RN101), DenseNet-169 (DN169), and Inception-v4 (Iv4). Adversarial images are generated by running attacks against the ResNet-50 model, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. Higher is better. The best defense against each attack is typeset in boldface.]]<br />
<br />
==GrayBox - Image Transformation at Training and Test Time ==<br />
In this experiment, the adversary has access to the network and the related parameters (but does not have access to the input transformations applied at test time). From the network trained in-(BlackBox: Image Transformation at Training and Test Time), novel adversarial images were generated by the four attack methods. The results show that Bit-Depth Reduction and JPEG Compression are weak defenses in such a gray box setting. In contrast, image cropping, rescaling, variation minimization, and image quilting are more robust against adversarial images in this setting.<br />
The results for this experiment are shown in below figure. Networks using these defenses classify up to 50 % of images correctly.<br />
<br />
[[File:sFig6.png|center| 600px |]]<br />
<br />
==Comparison With Ensemble Adversarial Training==<br />
The results of the experiment are compared with the state of the art ensemble adversarial training approach proposed by Tramer et al. [2]. Ensemble Training fits the parameters of a Convolutional Neural Network on adversarial examples that were generated to attack an ensemble of pre-trained models. The model release by Tramer et al [2]: an Inception-Resnet-v2, trained on adversarial examples generated by FGSM against Inception-Resnet-v2 and Inception-v3 models. The authors compared their ResNet-50 models with image cropping, total variance minimization and image quilting defenses. Two assumption differences need to be noticed. Their defenses assume the input transformation is unknown to the adversary and no prior knowledge of the attacks is being used. The results of ensemble training and the pre-processing techniques mentioned in this paper are shown in Table 2. The results show that ensemble adversarial training works better on FGSM attacks (which it uses at training time), but is outperformed by each of the transformation-based defenses all other attacks.<br />
<br />
<br />
<br />
[[File:sTab2.png|600px|thumb|center|Table 2. Top-1 classification accuracy on images perturbed using attacks against ResNet-50 models trained on input-transformed images and an Inception-v4 model trained using ensemble adversarial. Adversarial images are generated by running attacks against the models, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. The best defense against each attack is typeset in boldface.]]<br />
<br />
=Discussion/Conclusions=<br />
The paper proposed reasonable approaches to countering adversarial images. The authors evaluated Total Variance Minimization and Image Quilting and compared it with already proposed ideas like Image Cropping - Rescaling, Bit Depth Reduction, JPEG Compression, and Decompression on the challenging ImageNet dataset.<br />
Previous work by Wang et al. [10] shows that a strong input defense should be nondifferentiable and randomized. Two of the defenses - namely Total Variation Minimization and Image Quilting, both possess this property. However, it may still be possible to train a network to perhaps act as an approximation to the non-differentiable transformation. <br />
<br />
Image quilting involves a discrete variable that conducts the selection of a patch from the database, which is a non-differentiable operation.<br />
Additionally, total variation minimization randomly conducts pixels selection from the pixels it uses to measure reconstruction<br />
error during creation of the de-noised image. Image quilting conducts a random selection of a particular K<br />
nearest neighbor uniformly but in a random manner. This inherent randomness makes it difficult to attack the model. <br />
<br />
Future work suggests applying the same techniques to other domains such as speech recognition and image segmentation. For example, in speech recognition, total variance minimization can be used to remove perturbations from waveforms and "spectrogram quilting" techniques that reconstruct a spectrogram could be developed. The proposed input-transformation defenses can also be combined with ensemble adversarial training by Tramèr et al.[2] to study new attack methods.<br />
<br />
=Critiques=<br />
1. The terminology of Black Box, White Box, and Grey Box attack is not exactly given and clear.<br />
<br />
2. White Box attacks could have been considered where the adversary has a full access to the model as well as the pre-processing techniques.<br />
<br />
3. Though the authors did a considerable work in showing the effect of four attacks on ImageNet database, much stronger attacks (Madry et al) [7], could have been evaluated.<br />
<br />
4. Authors claim that the success rate is generally measured as a function of the magnitude of perturbations, performed by the attack using the L2- dissimilarity, but the claim is not supported by any references. None of the previous work has used these metrics.<br />
<br />
5. ([https://openreview.net/forum?id=SyJ7ClWCb])In the new draft of the paper, the authors add the sentence "our defenses assume that part of the defense strategy (viz., the input transformation) is unknown to the adversary".<br />
<br />
This is a completely unreasonable assumption. Any algorithm which hopes to be secure must allow the adversary to, at the very least, understand what the defense is that's being used. Consider a world where the defense here is implemented in practice: any attacker in the world could just go look up the paper, read the description of the algorithm, and know how it works.<br />
<br />
=References=<br />
<br />
1. Chuan Guo , Mayank Rana & Moustapha Ciss´e & Laurens van der Maaten , Countering Adversarial Images Using Input Transformations<br />
<br />
2. Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, Patrick McDaniel, Ensemble Adversarial Training: Attacks and defenses.<br />
<br />
3. Abigail Graese, Andras Rozsa, and Terrance E. Boult. Assessing threat of adversarial examples of deep neural networks. CoRR, abs/1610.04256, 2016. <br />
<br />
4. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Adversary resistant deep neural networks with an application to malware detection. CoRR, abs/1610.01239, 2016a.<br />
<br />
5. Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. CoRR, abs/1704.01155, 2017. <br />
<br />
6. Gintare Karolina Dziugaite, Zoubin Ghahramani, and Daniel Roy. A study of the effect of JPG compression on adversarial images. CoRR, abs/1608.00853, 2016.<br />
<br />
7. Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu .Towards Deep Learning Models Resistant to Adversarial Attacks, arXiv:1706.06083v3<br />
<br />
8. Alexei Efros and William Freeman. Image quilting for texture synthesis and transfer. In Proc. SIGGRAPH, pp. 341–346, 2001.<br />
<br />
9. Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.<br />
<br />
10. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Learning adversary-resistant deep neural networks. CoRR, abs/1612.01401, 2016b.<br />
<br />
11. Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. CoRR, abs/1611.02770, 2016.<br />
<br />
12. Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. CoRR, abs/1707.05373, 2017 <br />
<br />
13. Marco Melis, Ambra Demontis, Battista Biggio, Gavin Brown, Giorgio Fumera, and Fabio Roli. Is deep learning safe for robot vision? adversarial examples against the icub humanoid. CoRR,abs/1708.06939, 2017.<br />
<br />
14. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. Adversarial examples in the physical world. CoRR, abs/1607.02533, 2016b.<br />
<br />
15. Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: A simple and accurate method to fool deep neural networks. In Proc. CVPR, pp. 2574–2582, 2016.<br />
<br />
16. Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy, pp. 39–57, 2017.<br />
<br />
17. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In Proc. ICLR, 2015.<br />
<br />
18. Nicolas Papernot, Patrick McDaniel, Ian Goodfellow, Somesh Jha, Z Berkay Celik, and Ananthram Swami. Practical black-box attacks against machine learning. In ACM Asia Conference on Computer and Communications Security, 2017.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=42267Countering Adversarial Images Using Input Transformations2018-12-05T01:27:47Z<p>A22ravi: /* References */</p>
<hr />
<div>The code for this paper is available here[https://github.com/facebookresearch/adversarial_image_defenses]<br />
<br />
==Motivation ==<br />
As the use of machine intelligence has increased, robustness has become a critical feature to guarantee the reliability of deployed machine-learning systems. However, recent research has shown that existing models are not robust to small, adversarially designed perturbations to the input. Adversarial examples are inputs to Machine Learning models so that an attacker has intentionally designed to cause the model to make a mistake. Adversarially perturbed examples have been deployed to attack image classification services (Liu et al., 2016)[11], speech recognition systems (Cisse et al., 2017a)[12], and robot vision (Melis et al., 2017)[13]. The existence of these adversarial examples has motivated proposals for approaches that increase the robustness of learning systems to such examples. In the example below (Goodfellow et. al) [17], a small perturbation is applied to the original image of a panda, changing the prediction to a gibbon.<br />
<br />
[[File:Panda.png|center]]<br />
<br />
==Introduction==<br />
The paper studies strategies that defend against adversarial example attacks on image classification systems by transforming the images before feeding them to a Convolutional Network Classifier. <br />
Generally, defenses against adversarial examples fall into two main categories:<br />
<br />
# Model-Specific – They enforce model properties such as smoothness and invariance via the learning algorithm. <br />
# Model-Agnostic – They try to remove adversarial perturbations from the input. <br />
<br />
Model-specific defense strategies make strong assumptions about expected adversarial attacks. As a result, they violate the Kerckhoffs principle, which states that adversaries can circumvent model-specific defenses by simply changing how an attack is executed. This paper focuses on increasing the effectiveness of model-agnostic defense strategies. Specifically, they investigated the following image transformations as a means for protecting against adversarial images:<br />
<br />
# Image Cropping and Re-scaling (Graese et al, 2016). <br />
# Bit Depth Reduction (Xu et al, 2017) <br />
# JPEG Compression (Dziugaite et al, 2016) <br />
# Total Variance Minimization (Rudin et al, 1992) <br />
# Image Quilting (Efros & Freeman, 2001). <br />
<br />
These image transformations have been studied against Adversarial attacks such as the fast gradient sign method (Goodfelow et. al., 2015), its iterative extension (Kurakin et al., 2016a), Deepfool (Moosavi-Dezfooli et al., 2016), and the Carlini & Wagner (2017) <math>L_2</math>attack. <br />
<br />
The authors in this paper try to focus on increasing the effectiveness of model-agnostic defense strategies through approaches that:<br />
# remove the adversarial perturbations from input images,<br />
# maintain sufficient information in input images to correctly classify them,<br />
# and are still effective in situations where the adversary has information about the defense strategy being used.<br />
<br />
From their experiments, the strongest defenses are based on Total Variance Minimization and Image Quilting. These defenses are non-differentiable and inherently random which makes it difficult for an adversary to get around them.<br />
<br />
==Previous Work==<br />
Recently, a lot of research has focused on countering adversarial threats. Wang et al [4], proposed a new adversary resistant technique that obstructs attackers from constructing impactful adversarial images. This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which augments the training process but not only included adversarial images constructed from their model but also including adversarial images generated from an ensemble of other models. Their method implemented on an Inception V2 classifier finished 1st among 70 submissions of NIPS 2017 competition on Defenses against Adversarial Attacks. Graese, et al. [3], showed how input transformation such as shifting, blurring and noise can render the majority of the adversarial examples as non-adversarial. Xu et al.[5] demonstrated, how feature squeezing methods, such as reducing the color bit depth of each pixel and spatial smoothing, defends against attacks. Dziugaite et al [6], studied the effect of JPG compression on adversarial images. Chen et al. [7] introduce an advanced denoising algorithm with GAN based noise modeling in order to improve the blind denoising performance in low-level vision processing. The GAN is trained to estimate the noise distribution over the input noisy images and to generate noise samples. Although meant for image processing, this method can be generalized to target adversarial examples where the unknown noise generating algorithm can be leveraged.<br />
<br />
==Terminology==<br />
<br />
'''Gray Box Attack''' : Model Architecture and parameters are public.<br />
<br />
'''Black Box Attack''': Consider a weak adversary with access to the DNN output only. The adversary has no knowledge<br />
of the architectural choices made to design the DNN, which include the number, type, and size of layers, nor of<br />
the training data used to learn the DNN’s parameters. Such attacks are referred to as black box, where adversaries need<br />
not know internal details of a system to compromise it [].<br />
<br />
An interesting and important observation of adversarial examples is that they generally are not model or architecture specific. Adversarial examples generated for one neural network architecture will transfer very well to another architecture. In other words, if you wanted to trick a model you could create your own model and adversarial examples based off of it. Then these same adversarial examples will most probably trick the other model as well. This has huge implications as it means that it is possible to create adversarial examples for a completely black box model where we have no prior knowledge of the internal mechanics. [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]<br />
<br />
'''Non Targeted Adversarial Attack''': The goal of the attack is to modify a source image in a way such that the image will be classified incorrectly by the network.<br />
<br />
This is an example on non-targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:non-targeted O.JPG| 600px|center]]<br />
<br />
'''Targeted Adversarial Attack''': The goal of the attack is to modify a source image in way such that image will be classified as a ''target'' class by the network.<br />
<br />
This is an example on targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:Targeted O.JPG| 600px|center]]<br />
<br />
'''Defense''': A defense is a strategy that aims make the prediction on an adversarial example h(x') equal to the prediction on the corresponding clean example h(x).<br />
<br />
== Problem Definition ==<br />
The paper discusses non-targeted adversarial attacks for image recognition systems. Given image space <math>\mathcal{X} = [0,1]^{H \times W \times C}</math>, a source image <math>x \in \mathcal{X}</math>, and a classifier <math>h(.)</math>, a non-targeted adversarial example of <math>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity function <math>d(·, ·)</math> and <math>\rho \geq 0</math>. In the best case scenario, <math>d(·, ·)</math> measures the perceptual difference between the original image <math>x</math> and the perturbed image <math>x'</math>, but usually, Euclidean distance (<math>||x - x'||_2</math>) or the Chebyshov distance (<math>||x - x'||_{\infty}</math>) are used.<br />
<br />
From a set of N clean images <math>[{x_{1}, …, x_{N}}]</math>, an adversarial attack aims to generate <math>[{x'_{1}, …, x'_{N}}]</math> images, such that (<math>x'_{n}</math>) is an adversary of (<math>x_{n}</math>).<br />
<br />
The success rate of an attack is given as: <br />
<br />
<center><math><br />
\frac{1}{N}\sum_{n=1}^{N}I[h(x_n) &ne; h({x_n}^\prime)],<br />
</math></center><br />
<br />
which is the proportions of predictions that were altered by an attack.<br />
<br />
The success rate is generally measured as a function of the magnitude of perturbations performed by the attack. In this paper, L2 perturbations are used and are quantified using the normalized L2-dissimilarity metric:<br />
<math> \frac{1}{N} \sum_{n=1}^N{\frac{\vert \vert x_n - x'_n \vert \vert_2}{\vert \vert x_n \vert \vert_2}} </math><br />
<br />
A strong adversarial attack has a high rate, while its normalized L2-dissimilarity given by the above equation is less.<br />
<br />
In most practical settings, an adversary does not have direct access to the model <math>h(·)</math> and has to do a black-box attack. <br />
<br />
However, prior work has shown successful attacks by transferring adversarial examples generated for a separately-trained model to an unknown target model (Liu et al., 2016), thus allowing efficient black-box attack. <br />
<br />
As a result, the authors investigate both the black-box and a more difficult gray-box attack setting: the adversary has access to the model architecture and the model parameters, but<br />
is unaware of the defence strategy that is being used.<br />
<br />
A defence is an approach that aims make the prediction on an adversarial example <math>h(x')</math> equal to the prediction on the corresponding clean example <math>h(x)</math>. In this study, the authors focus on image transformation defenses <math>g(x)</math> that perform prediction via <math>h(g(x'))</math>. Ideally, <math>g(·)</math> is a complex, non-differentiable, and potentially stochastic function: this makes it difficult for an adversary to attack the prediction model <math>h(g(x))</math> even when the adversary knows both <math>h(·)</math> and <math>g(·)</math>.<br />
<br />
==Adversarial Attacks==<br />
<br />
Although the exact effect that adversarial examples have on the network is unknown, Ian Goodfellow et. al's Deep Learning book states that adversarial examples exploit the linearity of neural networks to perturb the cost function to force incorrect classifications. Images are often high resolution, and thus have thousands of pixels (millions for HD images). An epsilon ball perturbation when dimensionality is in the magnitude of thousands/millions greatly effects the cost function (especially if it increases loss at every pixel). Hence, although the following methods such as FGSM and Iterative FGSM are very straightforward, they greatly influence the network under a white box attack. <br />
<br />
For the experimental purposes, below 4 attacks have been studied in the paper:<br />
<br />
1. '''Fast Gradient Sign Method (FGSM; Goodfellow et al. (2015)) [17]''': Given a source input <math>x</math>, and true label <math>y</math>, and let <math>l(.,.)</math> be the differentiable loss function used to train the classifier <math>h(.)</math>. Then the corresponding adversarial example is given by:<br />
<br />
<math>x' = x + \epsilon \cdot sign(\nabla_x l(x, y))</math><br />
<br />
for some <math>\epsilon \gt 0</math> which controls the perturbation magnitude.<br />
<br />
2. '''Iterative FGSM ((I-FGSM; Kurakin et al. (2016b)) [14]''': iteratively applies the FGSM update, where M is the number of iterations. It is given as:<br />
<br />
<math>x^{(m)} = x^{(m-1)} + \epsilon \cdot sign(\nabla_{x^{m-1}} l(x^{m-1}, y))</math><br />
<br />
where <math>m = 1,...,M; x^{(0)} = x;</math> and <math>x' = x^{(M)}</math>. M is set such that <math>h(x) \neq h(x')</math>.<br />
<br />
Both FGSM and I-FGSM work by minimizing the Chebyshev distance between the inputs and the generated adversarial examples.<br />
<br />
3. '''DeepFool ((Moosavi-Dezfooliet al., 2016) [15]''': projects x onto a linearization of the decision boundary defined by binary classifier h(.) for M iterations. This can be particularly effictive when a network uses ReLU activation functions. It is given as:<br />
<br />
[[File:DeepFool.PNG|400px |]]<br />
<br />
4. '''Carlini-Wagner's L2 attack (CW-L2; Carlini & Wagner (2017)) [16]''': propose an optimization-based attack that combines a differentiable surrogate for the model’s classification accuracy with an L2-penalty term which encourages the adversary image to be close to the original image. Let <math>Z(x)</math> be the operation that computes the logit vector (i.e., the output before the softmax layer) for an input <math>x</math>, and <math>Z(x)_k</math> be the logit value corresponding to class <math>k</math>. The untargeted variant<br />
of CW-L2 finds a solution to the unconstrained optimization problem. It is given as:<br />
<br />
[[File:Carlini.PNG|500px |]]<br />
<br />
As mentioned earlier, the first two attacks minimize the Chebyshev distance whereas the last two attacks minimize the Euclidean distance between the inputs and the adversarial examples.<br />
<br />
All the methods described above maintain <math>x' \in \mathcal{X}</math> by performing value clipping. <br />
<br />
Below figure shows adversarial images and corresponding perturbations at five levels of normalized L2-dissimilarity for all four attacks, mentioned above.<br />
<br />
[[File:Strength.PNG|thumb|center| 600px |Figure 1: Adversarial images and corresponding perturbations at five levels of normalized L2- dissimilarity for all four attacks.]]<br />
<br />
==Defenses==<br />
Defense is a strategy that aims to make the prediction on an adversarial example equal to the prediction on the corresponding clean example, and the particular structure of adversarial perturbations <math> x-x' </math> have been shown in Figure 1.<br />
Five image transformations that alter the structure of these perturbations have been studied:<br />
# Image Cropping and Re-scaling, <br />
# Bit Depth Reduction, <br />
# JPEG Compression, <br />
# Total Variance Minimization, <br />
# Image Quilting.<br />
<br />
'''Image cropping and Rescaling''' has the effect of altering the spatial positioning of the adversarial perturbation. In this study, images are cropped and re-scaled during training time as part of data-augmentation. At test time, the predictions of randomly cropped are averaged.<br />
<br />
'''Bit Depth Reduction (Xu et. al) [5]''' performs a simple type of quantization that can remove small (adversarial) variations in pixel values from an image. Images are reduced to 3 bits in the experiment.<br />
<br />
'''JPEG Compression and Decompression (Dziugaite etal., 2016)''' removes small perturbations by performing simple quantization. The authors use a quality level of 75/100 in their experiments<br />
<br />
'''Total Variance Minimization (Rudin et. al) [9]''' :<br />
This combines pixel dropout with total variance minimization. This approach randomly selects a small set of pixels, and reconstructs the “simplest” image that is consistent with the selected pixels. The reconstructed image does not contain the adversarial perturbations because these perturbations tend to be small and localized.Specifically, we first select a random set of pixels by sampling a Bernoulli random variable <math>X(i; j; k)</math> for each pixel location <math>(i; j; k)</math>;we maintain a pixel when <math>(i; j; k)</math>= 1. Next, we use total variation, minimization to constructs an image z that is similar to the (perturbed) input image x for the selected<br />
set of pixels, whilst also being “simple” in terms of total variation by solving:<br />
<br />
[[File:TV!.png|300px|]] , <br />
<br />
where <math>TV_{p}(z)</math> represents <math>L_{p}</math> total variation of '''z''' :<br />
<br />
[[File:TV2.png|500px|]]<br />
<br />
The total variation (TV) measures the amount of fine-scale variation in the image z, as a result of which TV minimization encourages removal of small (adversarial) perturbations in the image. The objective function is convex in <math>z</math>, which makes solving for z straightforward. In the paper, p = 2 and a special-purpose solver based on the split Bregman method (Goldstein & Osher, 2009) to perform total variance minimization efficiently is employed.<br />
The effectiveness of TV minimization is illustrated by the images in the middle column of the figure below: in particular, note that the adversarial perturbations that were present in the background for the non- transformed image (see bottom-left image) have nearly completely disappeared in the TV-minimized adversarial image (bottom-center image). As expected, TV minimization also changes image structure in non-homogeneous regions of the image, but as these perturbations were not adversarially designed we expect the negative effect of these changes to be limited.<br />
<br />
[[File:tvx.png]]<br />
<br />
The figure above represents an illustration of total variance minimization and image quilting applied to an original and an adversarial image (produced using I-FGSM with ε = 0.03, corresponding to a normalized L2 - dissimilarity of 0.075). From left to right, the columns correspond to (1) no transformation, (2) total variance minimization, and (3) image quilting. From top to bottom, rows correspond to: (1) the original image, (2) the corresponding adversarial image produced by I-FGSM, and (3) the absolute difference between the two images above. Difference images were multiplied by a constant scaling factor to increase visibility.<br />
<br />
<br />
'''Image Quilting (Efros & Freeman, 2001) [8]'''<br />
Image Quilting is a non-parametric technique that synthesizes images by piecing together small patches that are taken from a database of image patches. The algorithm places appropriate patches in the database for a predefined set of grid points and computes minimum graph cuts in all overlapping boundary regions to remove edge artifacts. Image Quilting can be used to remove adversarial perturbations by constructing a patch database that only contains patches from "clean" images ( without adversarial perturbations); the patches used to create the synthesized image are selected by finding the K nearest neighbors ( in pixel space) of the corresponding patch from the adversarial image in the patch database, and picking one of these neighbors uniformly at random. The motivation for this defense is that resulting image only contains pixels that were not modified by the adversary - the database of real patches is unlikely to contain the structures that appear in adversarial images.<br />
<br />
If we take a look at the effect of image quilting in the above figure, although interpretation of these images is more complicated due to the quantization errors that image quilting introduces, we can still observe that the absolute differences between quilted original and the quilted adversarial image appear to be smaller in non-homogeneous regions of the image. Based on this observation the authors suggest that TV minimization and image quilting lead to inherently different defenses.<br />
<br />
=Experiments=<br />
<br />
Five experiments were performed to test the efficacy of defenses. The first four experiments consider gray and black box attacks. The gray-box attack applies defenses on input adversarial images for the convolutional networks. The adversary is able to read model architecture and parameters but not the defense strategy. The black-box attack replaces convolutional network by a trained network with image-transformations. The final experiment compares the authors' defenses with prior work. <br />
<br />
'''Set up:'''<br />
Experiments are performed on the ImageNet image classification dataset. The dataset comprises 1.2 million training images and 50,000 test images that correspond to one of 1000 classes. The adversarial images are produced by attacking a ResNet-50 model, with different kinds of attacks mentioned in Section5. The strength of an adversary is measured in terms of its normalized L2-dissimilarity. To produce the adversarial images, L2 dissimilarity for each of the attack was set as below:<br />
<br />
- FGSM. Increasing the step size <math>\epsilon</math>, increases the normalized L2-dissimilarity.<br />
<br />
- I-FGSM. We fix M=10, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- DeepFool. We fix M=5, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- CW-L2. We fix <math>k</math>=0 and <math>\lambda_{f}</math> =10, and multiply the resulting perturbation <br />
<br />
The hyperparameters of the defenses have been fixed in all the experiments. Specifically the pixel dropout probability was set to <math>p</math>=0.5 and regularization parameter of total variation minimizer <math>\lambda_{TV}</math>=0.03.<br />
<br />
Below figure shows the difference between the set up in different experiments below. The network is either trained on a) regular images or b) transformed images. The different settings are marked by 8.1, 8.2 and 8.3 <br />
[[File:models3.png |center]] <br />
<br />
==GrayBox - Image Transformation at Test Time== <br />
This experiment applies a transformation on adversarial images at test time before feeding them to a ResNet -50 which was trained to classify clean images. Below figure shows the results for five different transformations applied and their corresponding Top-1 accuracy. Few of the interesting observations from the plot are: All of the image transformations partly eliminate the effects of the attack, Crop ensemble gives the best accuracy around 40-60 percent, with an ensemble size of 30. The accuracy of Image Quilting Defense hardly deteriorates as the strength of the adversary increases. However, it does impact accuracy on non-adversarial examples.<br />
<br />
[[File:sFig4.png|center|600px |]]<br />
<br />
==BlackBox - Image Transformation at Training and Test Time==<br />
ResNet-50 model was trained on transformed ImageNet Training images. Before feeding the images to the network for training, standard data augmentation (from He et al) along with bit depth reduction, JPEG Compression, TV Minimization, or Image Quilting were applied on the images. The classification accuracy on the same adversarial images as in the previous case is shown Figure below. (Adversary cannot get this trained model to generate new images - Hence this is assumed as a Black Box setting!). Below figure concludes that training Convolutional Neural Networks on images that are transformed in the same way at test time, dramatically improves the effectiveness of all transformation defenses. Nearly 80 -90 % of the attacks are defended successfully, even when the L2- dissimilarity is high.<br />
<br />
<br />
[[File:sFig5.png|center|600px |]]<br />
<br />
<br />
==Blackbox - Ensembling==<br />
Four networks ResNet-50, ResNet-10, DenseNet-169, and Inception-v4 along with an ensemble of defenses were studied, as shown in Table 1. The adversarial images are produced by attacking a ResNet-50 model. The results in the table conclude that Inception-v4 performs best. This could be due to that network having a higher accuracy even in non-adversarial settings. The best ensemble of defenses achieves an accuracy of about 71% against all the other attacks. The attacks deteriorate the accuracy of the best defenses (a combination of cropping, TVM, image quilting, and model transfer) by at most 6%. Gains of 1-2% in classification accuracy could be found from ensembling different defenses, while gains of 2-3% were found from transferring attacks to different network architectures.<br />
<br />
<br />
[[File:sTab1.png|600px|thumb|center|Table 1. Top-1 classification accuracy of ensemble and model transfer defenses (columns) against four black-box attacks (rows). The four networks we use to classify images are ResNet-50 (RN50), ResNet-101 (RN101), DenseNet-169 (DN169), and Inception-v4 (Iv4). Adversarial images are generated by running attacks against the ResNet-50 model, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. Higher is better. The best defense against each attack is typeset in boldface.]]<br />
<br />
==GrayBox - Image Transformation at Training and Test Time ==<br />
In this experiment, the adversary has access to the network and the related parameters (but does not have access to the input transformations applied at test time). From the network trained in-(BlackBox: Image Transformation at Training and Test Time), novel adversarial images were generated by the four attack methods. The results show that Bit-Depth Reduction and JPEG Compression are weak defenses in such a gray box setting. In contrast, image cropping, rescaling, variation minimization, and image quilting are more robust against adversarial images in this setting.<br />
The results for this experiment are shown in below figure. Networks using these defenses classify up to 50 % of images correctly.<br />
<br />
[[File:sFig6.png|center| 600px |]]<br />
<br />
==Comparison With Ensemble Adversarial Training==<br />
The results of the experiment are compared with the state of the art ensemble adversarial training approach proposed by Tramer et al. [2]. Ensemble Training fits the parameters of a Convolutional Neural Network on adversarial examples that were generated to attack an ensemble of pre-trained models. The model release by Tramer et al [2]: an Inception-Resnet-v2, trained on adversarial examples generated by FGSM against Inception-Resnet-v2 and Inception-v3 models. The authors compared their ResNet-50 models with image cropping, total variance minimization and image quilting defenses. Two assumption differences need to be noticed. Their defenses assume the input transformation is unknown to the adversary and no prior knowledge of the attacks is being used. The results of ensemble training and the pre-processing techniques mentioned in this paper are shown in Table 2. The results show that ensemble adversarial training works better on FGSM attacks (which it uses at training time), but is outperformed by each of the transformation-based defenses all other attacks.<br />
<br />
<br />
<br />
[[File:sTab2.png|600px|thumb|center|Table 2. Top-1 classification accuracy on images perturbed using attacks against ResNet-50 models trained on input-transformed images and an Inception-v4 model trained using ensemble adversarial. Adversarial images are generated by running attacks against the models, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. The best defense against each attack is typeset in boldface.]]<br />
<br />
=Discussion/Conclusions=<br />
The paper proposed reasonable approaches to countering adversarial images. The authors evaluated Total Variance Minimization and Image Quilting and compared it with already proposed ideas like Image Cropping - Rescaling, Bit Depth Reduction, JPEG Compression, and Decompression on the challenging ImageNet dataset.<br />
Previous work by Wang et al. [10] shows that a strong input defense should be nondifferentiable and randomized. Two of the defenses - namely Total Variation Minimization and Image Quilting, both possess this property. However, it may still be possible to train a network to perhaps act as an approximation to the non-differentiable transformation. <br />
<br />
Image quilting involves a discrete variable that conducts the selection of a patch from the database, which is a non-differentiable operation.<br />
Additionally, total variation minimization randomly conducts pixels selection from the pixels it uses to measure reconstruction<br />
error during creation of the de-noised image. Image quilting conducts a random selection of a particular K<br />
nearest neighbor uniformly but in a random manner. This inherent randomness makes it difficult to attack the model. <br />
<br />
Future work suggests applying the same techniques to other domains such as speech recognition and image segmentation. For example, in speech recognition, total variance minimization can be used to remove perturbations from waveforms and "spectrogram quilting" techniques that reconstruct a spectrogram could be developed. The proposed input-transformation defenses can also be combined with ensemble adversarial training by Tramèr et al.[2] to study new attack methods.<br />
<br />
=Critiques=<br />
1. The terminology of Black Box, White Box, and Grey Box attack is not exactly given and clear.<br />
<br />
2. White Box attacks could have been considered where the adversary has a full access to the model as well as the pre-processing techniques.<br />
<br />
3. Though the authors did a considerable work in showing the effect of four attacks on ImageNet database, much stronger attacks (Madry et al) [7], could have been evaluated.<br />
<br />
4. Authors claim that the success rate is generally measured as a function of the magnitude of perturbations, performed by the attack using the L2- dissimilarity, but the claim is not supported by any references. None of the previous work has used these metrics.<br />
<br />
5. ([https://openreview.net/forum?id=SyJ7ClWCb])In the new draft of the paper, the authors add the sentence "our defenses assume that part of the defense strategy (viz., the input transformation) is unknown to the adversary".<br />
<br />
This is a completely unreasonable assumption. Any algorithm which hopes to be secure must allow the adversary to, at the very least, understand what the defense is that's being used. Consider a world where the defense here is implemented in practice: any attacker in the world could just go look up the paper, read the description of the algorithm, and know how it works.<br />
<br />
=References=<br />
<br />
1. Chuan Guo , Mayank Rana & Moustapha Ciss´e & Laurens van der Maaten , Countering Adversarial Images Using Input Transformations<br />
<br />
2. Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, Patrick McDaniel, Ensemble Adversarial Training: Attacks and defenses.<br />
<br />
3. Abigail Graese, Andras Rozsa, and Terrance E. Boult. Assessing threat of adversarial examples of deep neural networks. CoRR, abs/1610.04256, 2016. <br />
<br />
4. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Adversary resistant deep neural networks with an application to malware detection. CoRR, abs/1610.01239, 2016a.<br />
<br />
5. Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. CoRR, abs/1704.01155, 2017. <br />
<br />
6. Gintare Karolina Dziugaite, Zoubin Ghahramani, and Daniel Roy. A study of the effect of JPG compression on adversarial images. CoRR, abs/1608.00853, 2016.<br />
<br />
7. Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu .Towards Deep Learning Models Resistant to Adversarial Attacks, arXiv:1706.06083v3<br />
<br />
8. Alexei Efros and William Freeman. Image quilting for texture synthesis and transfer. In Proc. SIGGRAPH, pp. 341–346, 2001.<br />
<br />
9. Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.<br />
<br />
10. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Learning adversary-resistant deep neural networks. CoRR, abs/1612.01401, 2016b.<br />
<br />
11. Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. CoRR, abs/1611.02770, 2016.<br />
<br />
12. Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. CoRR, abs/1707.05373, 2017 <br />
<br />
13. Marco Melis, Ambra Demontis, Battista Biggio, Gavin Brown, Giorgio Fumera, and Fabio Roli. Is deep learning safe for robot vision? adversarial examples against the icub humanoid. CoRR,abs/1708.06939, 2017.<br />
<br />
14. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. Adversarial examples in the physical world. CoRR, abs/1607.02533, 2016b.<br />
<br />
15. Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: A simple and accurate method to fool deep neural networks. In Proc. CVPR, pp. 2574–2582, 2016.<br />
<br />
16. Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy, pp. 39–57, 2017.<br />
<br />
17. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In Proc. ICLR, 2015.<br />
<br />
18. Nicolas Papernot, Patrick McDaniel, Ian Goodfellow, Somesh Jha, Z Berkay Celik, and Ananthram Swami. Practical black-box attacks against machine learning. In ACM Asia Conference on Computer and Communications Security, 2017.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=42266Countering Adversarial Images Using Input Transformations2018-12-05T01:26:41Z<p>A22ravi: /* Terminology */</p>
<hr />
<div>The code for this paper is available here[https://github.com/facebookresearch/adversarial_image_defenses]<br />
<br />
==Motivation ==<br />
As the use of machine intelligence has increased, robustness has become a critical feature to guarantee the reliability of deployed machine-learning systems. However, recent research has shown that existing models are not robust to small, adversarially designed perturbations to the input. Adversarial examples are inputs to Machine Learning models so that an attacker has intentionally designed to cause the model to make a mistake. Adversarially perturbed examples have been deployed to attack image classification services (Liu et al., 2016)[11], speech recognition systems (Cisse et al., 2017a)[12], and robot vision (Melis et al., 2017)[13]. The existence of these adversarial examples has motivated proposals for approaches that increase the robustness of learning systems to such examples. In the example below (Goodfellow et. al) [17], a small perturbation is applied to the original image of a panda, changing the prediction to a gibbon.<br />
<br />
[[File:Panda.png|center]]<br />
<br />
==Introduction==<br />
The paper studies strategies that defend against adversarial example attacks on image classification systems by transforming the images before feeding them to a Convolutional Network Classifier. <br />
Generally, defenses against adversarial examples fall into two main categories:<br />
<br />
# Model-Specific – They enforce model properties such as smoothness and invariance via the learning algorithm. <br />
# Model-Agnostic – They try to remove adversarial perturbations from the input. <br />
<br />
Model-specific defense strategies make strong assumptions about expected adversarial attacks. As a result, they violate the Kerckhoffs principle, which states that adversaries can circumvent model-specific defenses by simply changing how an attack is executed. This paper focuses on increasing the effectiveness of model-agnostic defense strategies. Specifically, they investigated the following image transformations as a means for protecting against adversarial images:<br />
<br />
# Image Cropping and Re-scaling (Graese et al, 2016). <br />
# Bit Depth Reduction (Xu et al, 2017) <br />
# JPEG Compression (Dziugaite et al, 2016) <br />
# Total Variance Minimization (Rudin et al, 1992) <br />
# Image Quilting (Efros & Freeman, 2001). <br />
<br />
These image transformations have been studied against Adversarial attacks such as the fast gradient sign method (Goodfelow et. al., 2015), its iterative extension (Kurakin et al., 2016a), Deepfool (Moosavi-Dezfooli et al., 2016), and the Carlini & Wagner (2017) <math>L_2</math>attack. <br />
<br />
The authors in this paper try to focus on increasing the effectiveness of model-agnostic defense strategies through approaches that:<br />
# remove the adversarial perturbations from input images,<br />
# maintain sufficient information in input images to correctly classify them,<br />
# and are still effective in situations where the adversary has information about the defense strategy being used.<br />
<br />
From their experiments, the strongest defenses are based on Total Variance Minimization and Image Quilting. These defenses are non-differentiable and inherently random which makes it difficult for an adversary to get around them.<br />
<br />
==Previous Work==<br />
Recently, a lot of research has focused on countering adversarial threats. Wang et al [4], proposed a new adversary resistant technique that obstructs attackers from constructing impactful adversarial images. This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which augments the training process but not only included adversarial images constructed from their model but also including adversarial images generated from an ensemble of other models. Their method implemented on an Inception V2 classifier finished 1st among 70 submissions of NIPS 2017 competition on Defenses against Adversarial Attacks. Graese, et al. [3], showed how input transformation such as shifting, blurring and noise can render the majority of the adversarial examples as non-adversarial. Xu et al.[5] demonstrated, how feature squeezing methods, such as reducing the color bit depth of each pixel and spatial smoothing, defends against attacks. Dziugaite et al [6], studied the effect of JPG compression on adversarial images. Chen et al. [7] introduce an advanced denoising algorithm with GAN based noise modeling in order to improve the blind denoising performance in low-level vision processing. The GAN is trained to estimate the noise distribution over the input noisy images and to generate noise samples. Although meant for image processing, this method can be generalized to target adversarial examples where the unknown noise generating algorithm can be leveraged.<br />
<br />
==Terminology==<br />
<br />
'''Gray Box Attack''' : Model Architecture and parameters are public.<br />
<br />
'''Black Box Attack''': Consider a weak adversary with access to the DNN output only. The adversary has no knowledge<br />
of the architectural choices made to design the DNN, which include the number, type, and size of layers, nor of<br />
the training data used to learn the DNN’s parameters. Such attacks are referred to as black box, where adversaries need<br />
not know internal details of a system to compromise it [].<br />
<br />
An interesting and important observation of adversarial examples is that they generally are not model or architecture specific. Adversarial examples generated for one neural network architecture will transfer very well to another architecture. In other words, if you wanted to trick a model you could create your own model and adversarial examples based off of it. Then these same adversarial examples will most probably trick the other model as well. This has huge implications as it means that it is possible to create adversarial examples for a completely black box model where we have no prior knowledge of the internal mechanics. [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]<br />
<br />
'''Non Targeted Adversarial Attack''': The goal of the attack is to modify a source image in a way such that the image will be classified incorrectly by the network.<br />
<br />
This is an example on non-targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:non-targeted O.JPG| 600px|center]]<br />
<br />
'''Targeted Adversarial Attack''': The goal of the attack is to modify a source image in way such that image will be classified as a ''target'' class by the network.<br />
<br />
This is an example on targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:Targeted O.JPG| 600px|center]]<br />
<br />
'''Defense''': A defense is a strategy that aims make the prediction on an adversarial example h(x') equal to the prediction on the corresponding clean example h(x).<br />
<br />
== Problem Definition ==<br />
The paper discusses non-targeted adversarial attacks for image recognition systems. Given image space <math>\mathcal{X} = [0,1]^{H \times W \times C}</math>, a source image <math>x \in \mathcal{X}</math>, and a classifier <math>h(.)</math>, a non-targeted adversarial example of <math>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity function <math>d(·, ·)</math> and <math>\rho \geq 0</math>. In the best case scenario, <math>d(·, ·)</math> measures the perceptual difference between the original image <math>x</math> and the perturbed image <math>x'</math>, but usually, Euclidean distance (<math>||x - x'||_2</math>) or the Chebyshov distance (<math>||x - x'||_{\infty}</math>) are used.<br />
<br />
From a set of N clean images <math>[{x_{1}, …, x_{N}}]</math>, an adversarial attack aims to generate <math>[{x'_{1}, …, x'_{N}}]</math> images, such that (<math>x'_{n}</math>) is an adversary of (<math>x_{n}</math>).<br />
<br />
The success rate of an attack is given as: <br />
<br />
<center><math><br />
\frac{1}{N}\sum_{n=1}^{N}I[h(x_n) &ne; h({x_n}^\prime)],<br />
</math></center><br />
<br />
which is the proportions of predictions that were altered by an attack.<br />
<br />
The success rate is generally measured as a function of the magnitude of perturbations performed by the attack. In this paper, L2 perturbations are used and are quantified using the normalized L2-dissimilarity metric:<br />
<math> \frac{1}{N} \sum_{n=1}^N{\frac{\vert \vert x_n - x'_n \vert \vert_2}{\vert \vert x_n \vert \vert_2}} </math><br />
<br />
A strong adversarial attack has a high rate, while its normalized L2-dissimilarity given by the above equation is less.<br />
<br />
In most practical settings, an adversary does not have direct access to the model <math>h(·)</math> and has to do a black-box attack. <br />
<br />
However, prior work has shown successful attacks by transferring adversarial examples generated for a separately-trained model to an unknown target model (Liu et al., 2016), thus allowing efficient black-box attack. <br />
<br />
As a result, the authors investigate both the black-box and a more difficult gray-box attack setting: the adversary has access to the model architecture and the model parameters, but<br />
is unaware of the defence strategy that is being used.<br />
<br />
A defence is an approach that aims make the prediction on an adversarial example <math>h(x')</math> equal to the prediction on the corresponding clean example <math>h(x)</math>. In this study, the authors focus on image transformation defenses <math>g(x)</math> that perform prediction via <math>h(g(x'))</math>. Ideally, <math>g(·)</math> is a complex, non-differentiable, and potentially stochastic function: this makes it difficult for an adversary to attack the prediction model <math>h(g(x))</math> even when the adversary knows both <math>h(·)</math> and <math>g(·)</math>.<br />
<br />
==Adversarial Attacks==<br />
<br />
Although the exact effect that adversarial examples have on the network is unknown, Ian Goodfellow et. al's Deep Learning book states that adversarial examples exploit the linearity of neural networks to perturb the cost function to force incorrect classifications. Images are often high resolution, and thus have thousands of pixels (millions for HD images). An epsilon ball perturbation when dimensionality is in the magnitude of thousands/millions greatly effects the cost function (especially if it increases loss at every pixel). Hence, although the following methods such as FGSM and Iterative FGSM are very straightforward, they greatly influence the network under a white box attack. <br />
<br />
For the experimental purposes, below 4 attacks have been studied in the paper:<br />
<br />
1. '''Fast Gradient Sign Method (FGSM; Goodfellow et al. (2015)) [17]''': Given a source input <math>x</math>, and true label <math>y</math>, and let <math>l(.,.)</math> be the differentiable loss function used to train the classifier <math>h(.)</math>. Then the corresponding adversarial example is given by:<br />
<br />
<math>x' = x + \epsilon \cdot sign(\nabla_x l(x, y))</math><br />
<br />
for some <math>\epsilon \gt 0</math> which controls the perturbation magnitude.<br />
<br />
2. '''Iterative FGSM ((I-FGSM; Kurakin et al. (2016b)) [14]''': iteratively applies the FGSM update, where M is the number of iterations. It is given as:<br />
<br />
<math>x^{(m)} = x^{(m-1)} + \epsilon \cdot sign(\nabla_{x^{m-1}} l(x^{m-1}, y))</math><br />
<br />
where <math>m = 1,...,M; x^{(0)} = x;</math> and <math>x' = x^{(M)}</math>. M is set such that <math>h(x) \neq h(x')</math>.<br />
<br />
Both FGSM and I-FGSM work by minimizing the Chebyshev distance between the inputs and the generated adversarial examples.<br />
<br />
3. '''DeepFool ((Moosavi-Dezfooliet al., 2016) [15]''': projects x onto a linearization of the decision boundary defined by binary classifier h(.) for M iterations. This can be particularly effictive when a network uses ReLU activation functions. It is given as:<br />
<br />
[[File:DeepFool.PNG|400px |]]<br />
<br />
4. '''Carlini-Wagner's L2 attack (CW-L2; Carlini & Wagner (2017)) [16]''': propose an optimization-based attack that combines a differentiable surrogate for the model’s classification accuracy with an L2-penalty term which encourages the adversary image to be close to the original image. Let <math>Z(x)</math> be the operation that computes the logit vector (i.e., the output before the softmax layer) for an input <math>x</math>, and <math>Z(x)_k</math> be the logit value corresponding to class <math>k</math>. The untargeted variant<br />
of CW-L2 finds a solution to the unconstrained optimization problem. It is given as:<br />
<br />
[[File:Carlini.PNG|500px |]]<br />
<br />
As mentioned earlier, the first two attacks minimize the Chebyshev distance whereas the last two attacks minimize the Euclidean distance between the inputs and the adversarial examples.<br />
<br />
All the methods described above maintain <math>x' \in \mathcal{X}</math> by performing value clipping. <br />
<br />
Below figure shows adversarial images and corresponding perturbations at five levels of normalized L2-dissimilarity for all four attacks, mentioned above.<br />
<br />
[[File:Strength.PNG|thumb|center| 600px |Figure 1: Adversarial images and corresponding perturbations at five levels of normalized L2- dissimilarity for all four attacks.]]<br />
<br />
==Defenses==<br />
Defense is a strategy that aims to make the prediction on an adversarial example equal to the prediction on the corresponding clean example, and the particular structure of adversarial perturbations <math> x-x' </math> have been shown in Figure 1.<br />
Five image transformations that alter the structure of these perturbations have been studied:<br />
# Image Cropping and Re-scaling, <br />
# Bit Depth Reduction, <br />
# JPEG Compression, <br />
# Total Variance Minimization, <br />
# Image Quilting.<br />
<br />
'''Image cropping and Rescaling''' has the effect of altering the spatial positioning of the adversarial perturbation. In this study, images are cropped and re-scaled during training time as part of data-augmentation. At test time, the predictions of randomly cropped are averaged.<br />
<br />
'''Bit Depth Reduction (Xu et. al) [5]''' performs a simple type of quantization that can remove small (adversarial) variations in pixel values from an image. Images are reduced to 3 bits in the experiment.<br />
<br />
'''JPEG Compression and Decompression (Dziugaite etal., 2016)''' removes small perturbations by performing simple quantization. The authors use a quality level of 75/100 in their experiments<br />
<br />
'''Total Variance Minimization (Rudin et. al) [9]''' :<br />
This combines pixel dropout with total variance minimization. This approach randomly selects a small set of pixels, and reconstructs the “simplest” image that is consistent with the selected pixels. The reconstructed image does not contain the adversarial perturbations because these perturbations tend to be small and localized.Specifically, we first select a random set of pixels by sampling a Bernoulli random variable <math>X(i; j; k)</math> for each pixel location <math>(i; j; k)</math>;we maintain a pixel when <math>(i; j; k)</math>= 1. Next, we use total variation, minimization to constructs an image z that is similar to the (perturbed) input image x for the selected<br />
set of pixels, whilst also being “simple” in terms of total variation by solving:<br />
<br />
[[File:TV!.png|300px|]] , <br />
<br />
where <math>TV_{p}(z)</math> represents <math>L_{p}</math> total variation of '''z''' :<br />
<br />
[[File:TV2.png|500px|]]<br />
<br />
The total variation (TV) measures the amount of fine-scale variation in the image z, as a result of which TV minimization encourages removal of small (adversarial) perturbations in the image. The objective function is convex in <math>z</math>, which makes solving for z straightforward. In the paper, p = 2 and a special-purpose solver based on the split Bregman method (Goldstein & Osher, 2009) to perform total variance minimization efficiently is employed.<br />
The effectiveness of TV minimization is illustrated by the images in the middle column of the figure below: in particular, note that the adversarial perturbations that were present in the background for the non- transformed image (see bottom-left image) have nearly completely disappeared in the TV-minimized adversarial image (bottom-center image). As expected, TV minimization also changes image structure in non-homogeneous regions of the image, but as these perturbations were not adversarially designed we expect the negative effect of these changes to be limited.<br />
<br />
[[File:tvx.png]]<br />
<br />
The figure above represents an illustration of total variance minimization and image quilting applied to an original and an adversarial image (produced using I-FGSM with ε = 0.03, corresponding to a normalized L2 - dissimilarity of 0.075). From left to right, the columns correspond to (1) no transformation, (2) total variance minimization, and (3) image quilting. From top to bottom, rows correspond to: (1) the original image, (2) the corresponding adversarial image produced by I-FGSM, and (3) the absolute difference between the two images above. Difference images were multiplied by a constant scaling factor to increase visibility.<br />
<br />
<br />
'''Image Quilting (Efros & Freeman, 2001) [8]'''<br />
Image Quilting is a non-parametric technique that synthesizes images by piecing together small patches that are taken from a database of image patches. The algorithm places appropriate patches in the database for a predefined set of grid points and computes minimum graph cuts in all overlapping boundary regions to remove edge artifacts. Image Quilting can be used to remove adversarial perturbations by constructing a patch database that only contains patches from "clean" images ( without adversarial perturbations); the patches used to create the synthesized image are selected by finding the K nearest neighbors ( in pixel space) of the corresponding patch from the adversarial image in the patch database, and picking one of these neighbors uniformly at random. The motivation for this defense is that resulting image only contains pixels that were not modified by the adversary - the database of real patches is unlikely to contain the structures that appear in adversarial images.<br />
<br />
If we take a look at the effect of image quilting in the above figure, although interpretation of these images is more complicated due to the quantization errors that image quilting introduces, we can still observe that the absolute differences between quilted original and the quilted adversarial image appear to be smaller in non-homogeneous regions of the image. Based on this observation the authors suggest that TV minimization and image quilting lead to inherently different defenses.<br />
<br />
=Experiments=<br />
<br />
Five experiments were performed to test the efficacy of defenses. The first four experiments consider gray and black box attacks. The gray-box attack applies defenses on input adversarial images for the convolutional networks. The adversary is able to read model architecture and parameters but not the defense strategy. The black-box attack replaces convolutional network by a trained network with image-transformations. The final experiment compares the authors' defenses with prior work. <br />
<br />
'''Set up:'''<br />
Experiments are performed on the ImageNet image classification dataset. The dataset comprises 1.2 million training images and 50,000 test images that correspond to one of 1000 classes. The adversarial images are produced by attacking a ResNet-50 model, with different kinds of attacks mentioned in Section5. The strength of an adversary is measured in terms of its normalized L2-dissimilarity. To produce the adversarial images, L2 dissimilarity for each of the attack was set as below:<br />
<br />
- FGSM. Increasing the step size <math>\epsilon</math>, increases the normalized L2-dissimilarity.<br />
<br />
- I-FGSM. We fix M=10, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- DeepFool. We fix M=5, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- CW-L2. We fix <math>k</math>=0 and <math>\lambda_{f}</math> =10, and multiply the resulting perturbation <br />
<br />
The hyperparameters of the defenses have been fixed in all the experiments. Specifically the pixel dropout probability was set to <math>p</math>=0.5 and regularization parameter of total variation minimizer <math>\lambda_{TV}</math>=0.03.<br />
<br />
Below figure shows the difference between the set up in different experiments below. The network is either trained on a) regular images or b) transformed images. The different settings are marked by 8.1, 8.2 and 8.3 <br />
[[File:models3.png |center]] <br />
<br />
==GrayBox - Image Transformation at Test Time== <br />
This experiment applies a transformation on adversarial images at test time before feeding them to a ResNet -50 which was trained to classify clean images. Below figure shows the results for five different transformations applied and their corresponding Top-1 accuracy. Few of the interesting observations from the plot are: All of the image transformations partly eliminate the effects of the attack, Crop ensemble gives the best accuracy around 40-60 percent, with an ensemble size of 30. The accuracy of Image Quilting Defense hardly deteriorates as the strength of the adversary increases. However, it does impact accuracy on non-adversarial examples.<br />
<br />
[[File:sFig4.png|center|600px |]]<br />
<br />
==BlackBox - Image Transformation at Training and Test Time==<br />
ResNet-50 model was trained on transformed ImageNet Training images. Before feeding the images to the network for training, standard data augmentation (from He et al) along with bit depth reduction, JPEG Compression, TV Minimization, or Image Quilting were applied on the images. The classification accuracy on the same adversarial images as in the previous case is shown Figure below. (Adversary cannot get this trained model to generate new images - Hence this is assumed as a Black Box setting!). Below figure concludes that training Convolutional Neural Networks on images that are transformed in the same way at test time, dramatically improves the effectiveness of all transformation defenses. Nearly 80 -90 % of the attacks are defended successfully, even when the L2- dissimilarity is high.<br />
<br />
<br />
[[File:sFig5.png|center|600px |]]<br />
<br />
<br />
==Blackbox - Ensembling==<br />
Four networks ResNet-50, ResNet-10, DenseNet-169, and Inception-v4 along with an ensemble of defenses were studied, as shown in Table 1. The adversarial images are produced by attacking a ResNet-50 model. The results in the table conclude that Inception-v4 performs best. This could be due to that network having a higher accuracy even in non-adversarial settings. The best ensemble of defenses achieves an accuracy of about 71% against all the other attacks. The attacks deteriorate the accuracy of the best defenses (a combination of cropping, TVM, image quilting, and model transfer) by at most 6%. Gains of 1-2% in classification accuracy could be found from ensembling different defenses, while gains of 2-3% were found from transferring attacks to different network architectures.<br />
<br />
<br />
[[File:sTab1.png|600px|thumb|center|Table 1. Top-1 classification accuracy of ensemble and model transfer defenses (columns) against four black-box attacks (rows). The four networks we use to classify images are ResNet-50 (RN50), ResNet-101 (RN101), DenseNet-169 (DN169), and Inception-v4 (Iv4). Adversarial images are generated by running attacks against the ResNet-50 model, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. Higher is better. The best defense against each attack is typeset in boldface.]]<br />
<br />
==GrayBox - Image Transformation at Training and Test Time ==<br />
In this experiment, the adversary has access to the network and the related parameters (but does not have access to the input transformations applied at test time). From the network trained in-(BlackBox: Image Transformation at Training and Test Time), novel adversarial images were generated by the four attack methods. The results show that Bit-Depth Reduction and JPEG Compression are weak defenses in such a gray box setting. In contrast, image cropping, rescaling, variation minimization, and image quilting are more robust against adversarial images in this setting.<br />
The results for this experiment are shown in below figure. Networks using these defenses classify up to 50 % of images correctly.<br />
<br />
[[File:sFig6.png|center| 600px |]]<br />
<br />
==Comparison With Ensemble Adversarial Training==<br />
The results of the experiment are compared with the state of the art ensemble adversarial training approach proposed by Tramer et al. [2]. Ensemble Training fits the parameters of a Convolutional Neural Network on adversarial examples that were generated to attack an ensemble of pre-trained models. The model release by Tramer et al [2]: an Inception-Resnet-v2, trained on adversarial examples generated by FGSM against Inception-Resnet-v2 and Inception-v3 models. The authors compared their ResNet-50 models with image cropping, total variance minimization and image quilting defenses. Two assumption differences need to be noticed. Their defenses assume the input transformation is unknown to the adversary and no prior knowledge of the attacks is being used. The results of ensemble training and the pre-processing techniques mentioned in this paper are shown in Table 2. The results show that ensemble adversarial training works better on FGSM attacks (which it uses at training time), but is outperformed by each of the transformation-based defenses all other attacks.<br />
<br />
<br />
<br />
[[File:sTab2.png|600px|thumb|center|Table 2. Top-1 classification accuracy on images perturbed using attacks against ResNet-50 models trained on input-transformed images and an Inception-v4 model trained using ensemble adversarial. Adversarial images are generated by running attacks against the models, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. The best defense against each attack is typeset in boldface.]]<br />
<br />
=Discussion/Conclusions=<br />
The paper proposed reasonable approaches to countering adversarial images. The authors evaluated Total Variance Minimization and Image Quilting and compared it with already proposed ideas like Image Cropping - Rescaling, Bit Depth Reduction, JPEG Compression, and Decompression on the challenging ImageNet dataset.<br />
Previous work by Wang et al. [10] shows that a strong input defense should be nondifferentiable and randomized. Two of the defenses - namely Total Variation Minimization and Image Quilting, both possess this property. However, it may still be possible to train a network to perhaps act as an approximation to the non-differentiable transformation. <br />
<br />
Image quilting involves a discrete variable that conducts the selection of a patch from the database, which is a non-differentiable operation.<br />
Additionally, total variation minimization randomly conducts pixels selection from the pixels it uses to measure reconstruction<br />
error during creation of the de-noised image. Image quilting conducts a random selection of a particular K<br />
nearest neighbor uniformly but in a random manner. This inherent randomness makes it difficult to attack the model. <br />
<br />
Future work suggests applying the same techniques to other domains such as speech recognition and image segmentation. For example, in speech recognition, total variance minimization can be used to remove perturbations from waveforms and "spectrogram quilting" techniques that reconstruct a spectrogram could be developed. The proposed input-transformation defenses can also be combined with ensemble adversarial training by Tramèr et al.[2] to study new attack methods.<br />
<br />
=Critiques=<br />
1. The terminology of Black Box, White Box, and Grey Box attack is not exactly given and clear.<br />
<br />
2. White Box attacks could have been considered where the adversary has a full access to the model as well as the pre-processing techniques.<br />
<br />
3. Though the authors did a considerable work in showing the effect of four attacks on ImageNet database, much stronger attacks (Madry et al) [7], could have been evaluated.<br />
<br />
4. Authors claim that the success rate is generally measured as a function of the magnitude of perturbations, performed by the attack using the L2- dissimilarity, but the claim is not supported by any references. None of the previous work has used these metrics.<br />
<br />
5. ([https://openreview.net/forum?id=SyJ7ClWCb])In the new draft of the paper, the authors add the sentence "our defenses assume that part of the defense strategy (viz., the input transformation) is unknown to the adversary".<br />
<br />
This is a completely unreasonable assumption. Any algorithm which hopes to be secure must allow the adversary to, at the very least, understand what the defense is that's being used. Consider a world where the defense here is implemented in practice: any attacker in the world could just go look up the paper, read the description of the algorithm, and know how it works.<br />
<br />
=References=<br />
<br />
1. Chuan Guo , Mayank Rana & Moustapha Ciss´e & Laurens van der Maaten , Countering Adversarial Images Using Input Transformations<br />
<br />
2. Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, Patrick McDaniel, Ensemble Adversarial Training: Attacks and defenses.<br />
<br />
3. Abigail Graese, Andras Rozsa, and Terrance E. Boult. Assessing threat of adversarial examples of deep neural networks. CoRR, abs/1610.04256, 2016. <br />
<br />
4. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Adversary resistant deep neural networks with an application to malware detection. CoRR, abs/1610.01239, 2016a.<br />
<br />
5. Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. CoRR, abs/1704.01155, 2017. <br />
<br />
6. Gintare Karolina Dziugaite, Zoubin Ghahramani, and Daniel Roy. A study of the effect of JPG compression on adversarial images. CoRR, abs/1608.00853, 2016.<br />
<br />
7. Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu .Towards Deep Learning Models Resistant to Adversarial Attacks, arXiv:1706.06083v3<br />
<br />
8. Alexei Efros and William Freeman. Image quilting for texture synthesis and transfer. In Proc. SIGGRAPH, pp. 341–346, 2001.<br />
<br />
9. Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.<br />
<br />
10. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Learning adversary-resistant deep neural networks. CoRR, abs/1612.01401, 2016b.<br />
<br />
11. Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. CoRR, abs/1611.02770, 2016.<br />
<br />
12. Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. CoRR, abs/1707.05373, 2017 <br />
<br />
13. Marco Melis, Ambra Demontis, Battista Biggio, Gavin Brown, Giorgio Fumera, and Fabio Roli. Is deep learning safe for robot vision? adversarial examples against the icub humanoid. CoRR,abs/1708.06939, 2017.<br />
<br />
14. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. Adversarial examples in the physical world. CoRR, abs/1607.02533, 2016b.<br />
<br />
15. Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: A simple and accurate method to fool deep neural networks. In Proc. CVPR, pp. 2574–2582, 2016.<br />
<br />
16. Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy, pp. 39–57, 2017.<br />
<br />
17. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In Proc. ICLR, 2015.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=42265Countering Adversarial Images Using Input Transformations2018-12-05T01:15:42Z<p>A22ravi: /* Problem Definition */</p>
<hr />
<div>The code for this paper is available here[https://github.com/facebookresearch/adversarial_image_defenses]<br />
<br />
==Motivation ==<br />
As the use of machine intelligence has increased, robustness has become a critical feature to guarantee the reliability of deployed machine-learning systems. However, recent research has shown that existing models are not robust to small, adversarially designed perturbations to the input. Adversarial examples are inputs to Machine Learning models so that an attacker has intentionally designed to cause the model to make a mistake. Adversarially perturbed examples have been deployed to attack image classification services (Liu et al., 2016)[11], speech recognition systems (Cisse et al., 2017a)[12], and robot vision (Melis et al., 2017)[13]. The existence of these adversarial examples has motivated proposals for approaches that increase the robustness of learning systems to such examples. In the example below (Goodfellow et. al) [17], a small perturbation is applied to the original image of a panda, changing the prediction to a gibbon.<br />
<br />
[[File:Panda.png|center]]<br />
<br />
==Introduction==<br />
The paper studies strategies that defend against adversarial example attacks on image classification systems by transforming the images before feeding them to a Convolutional Network Classifier. <br />
Generally, defenses against adversarial examples fall into two main categories:<br />
<br />
# Model-Specific – They enforce model properties such as smoothness and invariance via the learning algorithm. <br />
# Model-Agnostic – They try to remove adversarial perturbations from the input. <br />
<br />
Model-specific defense strategies make strong assumptions about expected adversarial attacks. As a result, they violate the Kerckhoffs principle, which states that adversaries can circumvent model-specific defenses by simply changing how an attack is executed. This paper focuses on increasing the effectiveness of model-agnostic defense strategies. Specifically, they investigated the following image transformations as a means for protecting against adversarial images:<br />
<br />
# Image Cropping and Re-scaling (Graese et al, 2016). <br />
# Bit Depth Reduction (Xu et al, 2017) <br />
# JPEG Compression (Dziugaite et al, 2016) <br />
# Total Variance Minimization (Rudin et al, 1992) <br />
# Image Quilting (Efros & Freeman, 2001). <br />
<br />
These image transformations have been studied against Adversarial attacks such as the fast gradient sign method (Goodfelow et. al., 2015), its iterative extension (Kurakin et al., 2016a), Deepfool (Moosavi-Dezfooli et al., 2016), and the Carlini & Wagner (2017) <math>L_2</math>attack. <br />
<br />
The authors in this paper try to focus on increasing the effectiveness of model-agnostic defense strategies through approaches that:<br />
# remove the adversarial perturbations from input images,<br />
# maintain sufficient information in input images to correctly classify them,<br />
# and are still effective in situations where the adversary has information about the defense strategy being used.<br />
<br />
From their experiments, the strongest defenses are based on Total Variance Minimization and Image Quilting. These defenses are non-differentiable and inherently random which makes it difficult for an adversary to get around them.<br />
<br />
==Previous Work==<br />
Recently, a lot of research has focused on countering adversarial threats. Wang et al [4], proposed a new adversary resistant technique that obstructs attackers from constructing impactful adversarial images. This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which augments the training process but not only included adversarial images constructed from their model but also including adversarial images generated from an ensemble of other models. Their method implemented on an Inception V2 classifier finished 1st among 70 submissions of NIPS 2017 competition on Defenses against Adversarial Attacks. Graese, et al. [3], showed how input transformation such as shifting, blurring and noise can render the majority of the adversarial examples as non-adversarial. Xu et al.[5] demonstrated, how feature squeezing methods, such as reducing the color bit depth of each pixel and spatial smoothing, defends against attacks. Dziugaite et al [6], studied the effect of JPG compression on adversarial images. Chen et al. [7] introduce an advanced denoising algorithm with GAN based noise modeling in order to improve the blind denoising performance in low-level vision processing. The GAN is trained to estimate the noise distribution over the input noisy images and to generate noise samples. Although meant for image processing, this method can be generalized to target adversarial examples where the unknown noise generating algorithm can be leveraged.<br />
<br />
==Terminology==<br />
<br />
'''Gray Box Attack''' : Model Architecture and parameters are public.<br />
<br />
'''Black Box Attack''': Adversary does not have access to the model.<br />
<br />
An interesting and important observation of adversarial examples is that they generally are not model or architecture specific. Adversarial examples generated for one neural network architecture will transfer very well to another architecture. In other words, if you wanted to trick a model you could create your own model and adversarial examples based off of it. Then these same adversarial examples will most probably trick the other model as well. This has huge implications as it means that it is possible to create adversarial examples for a completely black box model where we have no prior knowledge of the internal mechanics. [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]<br />
<br />
'''Non Targeted Adversarial Attack''': The goal of the attack is to modify a source image in a way such that the image will be classified incorrectly by the network.<br />
<br />
This is an example on non-targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:non-targeted O.JPG| 600px|center]]<br />
<br />
'''Targeted Adversarial Attack''': The goal of the attack is to modify a source image in way such that image will be classified as a ''target'' class by the network.<br />
<br />
This is an example on targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:Targeted O.JPG| 600px|center]]<br />
<br />
'''Defense''': A defense is a strategy that aims make the prediction on an adversarial example h(x') equal to the prediction on the corresponding clean example h(x).<br />
<br />
== Problem Definition ==<br />
The paper discusses non-targeted adversarial attacks for image recognition systems. Given image space <math>\mathcal{X} = [0,1]^{H \times W \times C}</math>, a source image <math>x \in \mathcal{X}</math>, and a classifier <math>h(.)</math>, a non-targeted adversarial example of <math>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity function <math>d(·, ·)</math> and <math>\rho \geq 0</math>. In the best case scenario, <math>d(·, ·)</math> measures the perceptual difference between the original image <math>x</math> and the perturbed image <math>x'</math>, but usually, Euclidean distance (<math>||x - x'||_2</math>) or the Chebyshov distance (<math>||x - x'||_{\infty}</math>) are used.<br />
<br />
From a set of N clean images <math>[{x_{1}, …, x_{N}}]</math>, an adversarial attack aims to generate <math>[{x'_{1}, …, x'_{N}}]</math> images, such that (<math>x'_{n}</math>) is an adversary of (<math>x_{n}</math>).<br />
<br />
The success rate of an attack is given as: <br />
<br />
<center><math><br />
\frac{1}{N}\sum_{n=1}^{N}I[h(x_n) &ne; h({x_n}^\prime)],<br />
</math></center><br />
<br />
which is the proportions of predictions that were altered by an attack.<br />
<br />
The success rate is generally measured as a function of the magnitude of perturbations performed by the attack. In this paper, L2 perturbations are used and are quantified using the normalized L2-dissimilarity metric:<br />
<math> \frac{1}{N} \sum_{n=1}^N{\frac{\vert \vert x_n - x'_n \vert \vert_2}{\vert \vert x_n \vert \vert_2}} </math><br />
<br />
A strong adversarial attack has a high rate, while its normalized L2-dissimilarity given by the above equation is less.<br />
<br />
In most practical settings, an adversary does not have direct access to the model <math>h(·)</math> and has to do a black-box attack. <br />
<br />
However, prior work has shown successful attacks by transferring adversarial examples generated for a separately-trained model to an unknown target model (Liu et al., 2016), thus allowing efficient black-box attack. <br />
<br />
As a result, the authors investigate both the black-box and a more difficult gray-box attack setting: the adversary has access to the model architecture and the model parameters, but<br />
is unaware of the defence strategy that is being used.<br />
<br />
A defence is an approach that aims make the prediction on an adversarial example <math>h(x')</math> equal to the prediction on the corresponding clean example <math>h(x)</math>. In this study, the authors focus on image transformation defenses <math>g(x)</math> that perform prediction via <math>h(g(x'))</math>. Ideally, <math>g(·)</math> is a complex, non-differentiable, and potentially stochastic function: this makes it difficult for an adversary to attack the prediction model <math>h(g(x))</math> even when the adversary knows both <math>h(·)</math> and <math>g(·)</math>.<br />
<br />
==Adversarial Attacks==<br />
<br />
Although the exact effect that adversarial examples have on the network is unknown, Ian Goodfellow et. al's Deep Learning book states that adversarial examples exploit the linearity of neural networks to perturb the cost function to force incorrect classifications. Images are often high resolution, and thus have thousands of pixels (millions for HD images). An epsilon ball perturbation when dimensionality is in the magnitude of thousands/millions greatly effects the cost function (especially if it increases loss at every pixel). Hence, although the following methods such as FGSM and Iterative FGSM are very straightforward, they greatly influence the network under a white box attack. <br />
<br />
For the experimental purposes, below 4 attacks have been studied in the paper:<br />
<br />
1. '''Fast Gradient Sign Method (FGSM; Goodfellow et al. (2015)) [17]''': Given a source input <math>x</math>, and true label <math>y</math>, and let <math>l(.,.)</math> be the differentiable loss function used to train the classifier <math>h(.)</math>. Then the corresponding adversarial example is given by:<br />
<br />
<math>x' = x + \epsilon \cdot sign(\nabla_x l(x, y))</math><br />
<br />
for some <math>\epsilon \gt 0</math> which controls the perturbation magnitude.<br />
<br />
2. '''Iterative FGSM ((I-FGSM; Kurakin et al. (2016b)) [14]''': iteratively applies the FGSM update, where M is the number of iterations. It is given as:<br />
<br />
<math>x^{(m)} = x^{(m-1)} + \epsilon \cdot sign(\nabla_{x^{m-1}} l(x^{m-1}, y))</math><br />
<br />
where <math>m = 1,...,M; x^{(0)} = x;</math> and <math>x' = x^{(M)}</math>. M is set such that <math>h(x) \neq h(x')</math>.<br />
<br />
Both FGSM and I-FGSM work by minimizing the Chebyshev distance between the inputs and the generated adversarial examples.<br />
<br />
3. '''DeepFool ((Moosavi-Dezfooliet al., 2016) [15]''': projects x onto a linearization of the decision boundary defined by binary classifier h(.) for M iterations. This can be particularly effictive when a network uses ReLU activation functions. It is given as:<br />
<br />
[[File:DeepFool.PNG|400px |]]<br />
<br />
4. '''Carlini-Wagner's L2 attack (CW-L2; Carlini & Wagner (2017)) [16]''': propose an optimization-based attack that combines a differentiable surrogate for the model’s classification accuracy with an L2-penalty term which encourages the adversary image to be close to the original image. Let <math>Z(x)</math> be the operation that computes the logit vector (i.e., the output before the softmax layer) for an input <math>x</math>, and <math>Z(x)_k</math> be the logit value corresponding to class <math>k</math>. The untargeted variant<br />
of CW-L2 finds a solution to the unconstrained optimization problem. It is given as:<br />
<br />
[[File:Carlini.PNG|500px |]]<br />
<br />
As mentioned earlier, the first two attacks minimize the Chebyshev distance whereas the last two attacks minimize the Euclidean distance between the inputs and the adversarial examples.<br />
<br />
All the methods described above maintain <math>x' \in \mathcal{X}</math> by performing value clipping. <br />
<br />
Below figure shows adversarial images and corresponding perturbations at five levels of normalized L2-dissimilarity for all four attacks, mentioned above.<br />
<br />
[[File:Strength.PNG|thumb|center| 600px |Figure 1: Adversarial images and corresponding perturbations at five levels of normalized L2- dissimilarity for all four attacks.]]<br />
<br />
==Defenses==<br />
Defense is a strategy that aims to make the prediction on an adversarial example equal to the prediction on the corresponding clean example, and the particular structure of adversarial perturbations <math> x-x' </math> have been shown in Figure 1.<br />
Five image transformations that alter the structure of these perturbations have been studied:<br />
# Image Cropping and Re-scaling, <br />
# Bit Depth Reduction, <br />
# JPEG Compression, <br />
# Total Variance Minimization, <br />
# Image Quilting.<br />
<br />
'''Image cropping and Rescaling''' has the effect of altering the spatial positioning of the adversarial perturbation. In this study, images are cropped and re-scaled during training time as part of data-augmentation. At test time, the predictions of randomly cropped are averaged.<br />
<br />
'''Bit Depth Reduction (Xu et. al) [5]''' performs a simple type of quantization that can remove small (adversarial) variations in pixel values from an image. Images are reduced to 3 bits in the experiment.<br />
<br />
'''JPEG Compression and Decompression (Dziugaite etal., 2016)''' removes small perturbations by performing simple quantization. The authors use a quality level of 75/100 in their experiments<br />
<br />
'''Total Variance Minimization (Rudin et. al) [9]''' :<br />
This combines pixel dropout with total variance minimization. This approach randomly selects a small set of pixels, and reconstructs the “simplest” image that is consistent with the selected pixels. The reconstructed image does not contain the adversarial perturbations because these perturbations tend to be small and localized.Specifically, we first select a random set of pixels by sampling a Bernoulli random variable <math>X(i; j; k)</math> for each pixel location <math>(i; j; k)</math>;we maintain a pixel when <math>(i; j; k)</math>= 1. Next, we use total variation, minimization to constructs an image z that is similar to the (perturbed) input image x for the selected<br />
set of pixels, whilst also being “simple” in terms of total variation by solving:<br />
<br />
[[File:TV!.png|300px|]] , <br />
<br />
where <math>TV_{p}(z)</math> represents <math>L_{p}</math> total variation of '''z''' :<br />
<br />
[[File:TV2.png|500px|]]<br />
<br />
The total variation (TV) measures the amount of fine-scale variation in the image z, as a result of which TV minimization encourages removal of small (adversarial) perturbations in the image. The objective function is convex in <math>z</math>, which makes solving for z straightforward. In the paper, p = 2 and a special-purpose solver based on the split Bregman method (Goldstein & Osher, 2009) to perform total variance minimization efficiently is employed.<br />
The effectiveness of TV minimization is illustrated by the images in the middle column of the figure below: in particular, note that the adversarial perturbations that were present in the background for the non- transformed image (see bottom-left image) have nearly completely disappeared in the TV-minimized adversarial image (bottom-center image). As expected, TV minimization also changes image structure in non-homogeneous regions of the image, but as these perturbations were not adversarially designed we expect the negative effect of these changes to be limited.<br />
<br />
[[File:tvx.png]]<br />
<br />
The figure above represents an illustration of total variance minimization and image quilting applied to an original and an adversarial image (produced using I-FGSM with ε = 0.03, corresponding to a normalized L2 - dissimilarity of 0.075). From left to right, the columns correspond to (1) no transformation, (2) total variance minimization, and (3) image quilting. From top to bottom, rows correspond to: (1) the original image, (2) the corresponding adversarial image produced by I-FGSM, and (3) the absolute difference between the two images above. Difference images were multiplied by a constant scaling factor to increase visibility.<br />
<br />
<br />
'''Image Quilting (Efros & Freeman, 2001) [8]'''<br />
Image Quilting is a non-parametric technique that synthesizes images by piecing together small patches that are taken from a database of image patches. The algorithm places appropriate patches in the database for a predefined set of grid points and computes minimum graph cuts in all overlapping boundary regions to remove edge artifacts. Image Quilting can be used to remove adversarial perturbations by constructing a patch database that only contains patches from "clean" images ( without adversarial perturbations); the patches used to create the synthesized image are selected by finding the K nearest neighbors ( in pixel space) of the corresponding patch from the adversarial image in the patch database, and picking one of these neighbors uniformly at random. The motivation for this defense is that resulting image only contains pixels that were not modified by the adversary - the database of real patches is unlikely to contain the structures that appear in adversarial images.<br />
<br />
If we take a look at the effect of image quilting in the above figure, although interpretation of these images is more complicated due to the quantization errors that image quilting introduces, we can still observe that the absolute differences between quilted original and the quilted adversarial image appear to be smaller in non-homogeneous regions of the image. Based on this observation the authors suggest that TV minimization and image quilting lead to inherently different defenses.<br />
<br />
=Experiments=<br />
<br />
Five experiments were performed to test the efficacy of defenses. The first four experiments consider gray and black box attacks. The gray-box attack applies defenses on input adversarial images for the convolutional networks. The adversary is able to read model architecture and parameters but not the defense strategy. The black-box attack replaces convolutional network by a trained network with image-transformations. The final experiment compares the authors' defenses with prior work. <br />
<br />
'''Set up:'''<br />
Experiments are performed on the ImageNet image classification dataset. The dataset comprises 1.2 million training images and 50,000 test images that correspond to one of 1000 classes. The adversarial images are produced by attacking a ResNet-50 model, with different kinds of attacks mentioned in Section5. The strength of an adversary is measured in terms of its normalized L2-dissimilarity. To produce the adversarial images, L2 dissimilarity for each of the attack was set as below:<br />
<br />
- FGSM. Increasing the step size <math>\epsilon</math>, increases the normalized L2-dissimilarity.<br />
<br />
- I-FGSM. We fix M=10, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- DeepFool. We fix M=5, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- CW-L2. We fix <math>k</math>=0 and <math>\lambda_{f}</math> =10, and multiply the resulting perturbation <br />
<br />
The hyperparameters of the defenses have been fixed in all the experiments. Specifically the pixel dropout probability was set to <math>p</math>=0.5 and regularization parameter of total variation minimizer <math>\lambda_{TV}</math>=0.03.<br />
<br />
Below figure shows the difference between the set up in different experiments below. The network is either trained on a) regular images or b) transformed images. The different settings are marked by 8.1, 8.2 and 8.3 <br />
[[File:models3.png |center]] <br />
<br />
==GrayBox - Image Transformation at Test Time== <br />
This experiment applies a transformation on adversarial images at test time before feeding them to a ResNet -50 which was trained to classify clean images. Below figure shows the results for five different transformations applied and their corresponding Top-1 accuracy. Few of the interesting observations from the plot are: All of the image transformations partly eliminate the effects of the attack, Crop ensemble gives the best accuracy around 40-60 percent, with an ensemble size of 30. The accuracy of Image Quilting Defense hardly deteriorates as the strength of the adversary increases. However, it does impact accuracy on non-adversarial examples.<br />
<br />
[[File:sFig4.png|center|600px |]]<br />
<br />
==BlackBox - Image Transformation at Training and Test Time==<br />
ResNet-50 model was trained on transformed ImageNet Training images. Before feeding the images to the network for training, standard data augmentation (from He et al) along with bit depth reduction, JPEG Compression, TV Minimization, or Image Quilting were applied on the images. The classification accuracy on the same adversarial images as in the previous case is shown Figure below. (Adversary cannot get this trained model to generate new images - Hence this is assumed as a Black Box setting!). Below figure concludes that training Convolutional Neural Networks on images that are transformed in the same way at test time, dramatically improves the effectiveness of all transformation defenses. Nearly 80 -90 % of the attacks are defended successfully, even when the L2- dissimilarity is high.<br />
<br />
<br />
[[File:sFig5.png|center|600px |]]<br />
<br />
<br />
==Blackbox - Ensembling==<br />
Four networks ResNet-50, ResNet-10, DenseNet-169, and Inception-v4 along with an ensemble of defenses were studied, as shown in Table 1. The adversarial images are produced by attacking a ResNet-50 model. The results in the table conclude that Inception-v4 performs best. This could be due to that network having a higher accuracy even in non-adversarial settings. The best ensemble of defenses achieves an accuracy of about 71% against all the other attacks. The attacks deteriorate the accuracy of the best defenses (a combination of cropping, TVM, image quilting, and model transfer) by at most 6%. Gains of 1-2% in classification accuracy could be found from ensembling different defenses, while gains of 2-3% were found from transferring attacks to different network architectures.<br />
<br />
<br />
[[File:sTab1.png|600px|thumb|center|Table 1. Top-1 classification accuracy of ensemble and model transfer defenses (columns) against four black-box attacks (rows). The four networks we use to classify images are ResNet-50 (RN50), ResNet-101 (RN101), DenseNet-169 (DN169), and Inception-v4 (Iv4). Adversarial images are generated by running attacks against the ResNet-50 model, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. Higher is better. The best defense against each attack is typeset in boldface.]]<br />
<br />
==GrayBox - Image Transformation at Training and Test Time ==<br />
In this experiment, the adversary has access to the network and the related parameters (but does not have access to the input transformations applied at test time). From the network trained in-(BlackBox: Image Transformation at Training and Test Time), novel adversarial images were generated by the four attack methods. The results show that Bit-Depth Reduction and JPEG Compression are weak defenses in such a gray box setting. In contrast, image cropping, rescaling, variation minimization, and image quilting are more robust against adversarial images in this setting.<br />
The results for this experiment are shown in below figure. Networks using these defenses classify up to 50 % of images correctly.<br />
<br />
[[File:sFig6.png|center| 600px |]]<br />
<br />
==Comparison With Ensemble Adversarial Training==<br />
The results of the experiment are compared with the state of the art ensemble adversarial training approach proposed by Tramer et al. [2]. Ensemble Training fits the parameters of a Convolutional Neural Network on adversarial examples that were generated to attack an ensemble of pre-trained models. The model release by Tramer et al [2]: an Inception-Resnet-v2, trained on adversarial examples generated by FGSM against Inception-Resnet-v2 and Inception-v3 models. The authors compared their ResNet-50 models with image cropping, total variance minimization and image quilting defenses. Two assumption differences need to be noticed. Their defenses assume the input transformation is unknown to the adversary and no prior knowledge of the attacks is being used. The results of ensemble training and the pre-processing techniques mentioned in this paper are shown in Table 2. The results show that ensemble adversarial training works better on FGSM attacks (which it uses at training time), but is outperformed by each of the transformation-based defenses all other attacks.<br />
<br />
<br />
<br />
[[File:sTab2.png|600px|thumb|center|Table 2. Top-1 classification accuracy on images perturbed using attacks against ResNet-50 models trained on input-transformed images and an Inception-v4 model trained using ensemble adversarial. Adversarial images are generated by running attacks against the models, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. The best defense against each attack is typeset in boldface.]]<br />
<br />
=Discussion/Conclusions=<br />
The paper proposed reasonable approaches to countering adversarial images. The authors evaluated Total Variance Minimization and Image Quilting and compared it with already proposed ideas like Image Cropping - Rescaling, Bit Depth Reduction, JPEG Compression, and Decompression on the challenging ImageNet dataset.<br />
Previous work by Wang et al. [10] shows that a strong input defense should be nondifferentiable and randomized. Two of the defenses - namely Total Variation Minimization and Image Quilting, both possess this property. However, it may still be possible to train a network to perhaps act as an approximation to the non-differentiable transformation. <br />
<br />
Image quilting involves a discrete variable that conducts the selection of a patch from the database, which is a non-differentiable operation.<br />
Additionally, total variation minimization randomly conducts pixels selection from the pixels it uses to measure reconstruction<br />
error during creation of the de-noised image. Image quilting conducts a random selection of a particular K<br />
nearest neighbor uniformly but in a random manner. This inherent randomness makes it difficult to attack the model. <br />
<br />
Future work suggests applying the same techniques to other domains such as speech recognition and image segmentation. For example, in speech recognition, total variance minimization can be used to remove perturbations from waveforms and "spectrogram quilting" techniques that reconstruct a spectrogram could be developed. The proposed input-transformation defenses can also be combined with ensemble adversarial training by Tramèr et al.[2] to study new attack methods.<br />
<br />
=Critiques=<br />
1. The terminology of Black Box, White Box, and Grey Box attack is not exactly given and clear.<br />
<br />
2. White Box attacks could have been considered where the adversary has a full access to the model as well as the pre-processing techniques.<br />
<br />
3. Though the authors did a considerable work in showing the effect of four attacks on ImageNet database, much stronger attacks (Madry et al) [7], could have been evaluated.<br />
<br />
4. Authors claim that the success rate is generally measured as a function of the magnitude of perturbations, performed by the attack using the L2- dissimilarity, but the claim is not supported by any references. None of the previous work has used these metrics.<br />
<br />
5. ([https://openreview.net/forum?id=SyJ7ClWCb])In the new draft of the paper, the authors add the sentence "our defenses assume that part of the defense strategy (viz., the input transformation) is unknown to the adversary".<br />
<br />
This is a completely unreasonable assumption. Any algorithm which hopes to be secure must allow the adversary to, at the very least, understand what the defense is that's being used. Consider a world where the defense here is implemented in practice: any attacker in the world could just go look up the paper, read the description of the algorithm, and know how it works.<br />
<br />
=References=<br />
<br />
1. Chuan Guo , Mayank Rana & Moustapha Ciss´e & Laurens van der Maaten , Countering Adversarial Images Using Input Transformations<br />
<br />
2. Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, Patrick McDaniel, Ensemble Adversarial Training: Attacks and defenses.<br />
<br />
3. Abigail Graese, Andras Rozsa, and Terrance E. Boult. Assessing threat of adversarial examples of deep neural networks. CoRR, abs/1610.04256, 2016. <br />
<br />
4. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Adversary resistant deep neural networks with an application to malware detection. CoRR, abs/1610.01239, 2016a.<br />
<br />
5. Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. CoRR, abs/1704.01155, 2017. <br />
<br />
6. Gintare Karolina Dziugaite, Zoubin Ghahramani, and Daniel Roy. A study of the effect of JPG compression on adversarial images. CoRR, abs/1608.00853, 2016.<br />
<br />
7. Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu .Towards Deep Learning Models Resistant to Adversarial Attacks, arXiv:1706.06083v3<br />
<br />
8. Alexei Efros and William Freeman. Image quilting for texture synthesis and transfer. In Proc. SIGGRAPH, pp. 341–346, 2001.<br />
<br />
9. Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.<br />
<br />
10. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Learning adversary-resistant deep neural networks. CoRR, abs/1612.01401, 2016b.<br />
<br />
11. Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. CoRR, abs/1611.02770, 2016.<br />
<br />
12. Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. CoRR, abs/1707.05373, 2017 <br />
<br />
13. Marco Melis, Ambra Demontis, Battista Biggio, Gavin Brown, Giorgio Fumera, and Fabio Roli. Is deep learning safe for robot vision? adversarial examples against the icub humanoid. CoRR,abs/1708.06939, 2017.<br />
<br />
14. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. Adversarial examples in the physical world. CoRR, abs/1607.02533, 2016b.<br />
<br />
15. Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: A simple and accurate method to fool deep neural networks. In Proc. CVPR, pp. 2574–2582, 2016.<br />
<br />
16. Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy, pp. 39–57, 2017.<br />
<br />
17. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In Proc. ICLR, 2015.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Synthesizing_Programs_for_Images_usingReinforced_Adversarial_Learning&diff=42258Synthesizing Programs for Images usingReinforced Adversarial Learning2018-12-04T18:52:52Z<p>A22ravi: /* Critique and Future Work */</p>
<hr />
<div>'''Synthesizing Programs for Images using Reinforced Adversarial Learning: ''' Summary of the ICML 2018 paper <br />
<br />
Paper: [[http://proceedings.mlr.press/v80/ganin18a.html]]<br />
Video: [[https://www.youtube.com/watch?v=iSyvwAwa7vk&feature=youtu.be]]<br />
<br />
== Presented by ==<br />
<br />
1. Nekoei, Hadi [Quest ID: 20727088]<br />
<br />
= Motivation =<br />
<br />
Conventional neural generative models have major problems. <br />
<br />
* It is not clear how to inject knowledge about the data into the model. <br />
<br />
* Latent space is not easily interpretative. <br />
<br />
The provided solution in this paper is to generate programs to incorporate tools, e.g. graphics editors, illustration software, CAD. and '''creating more meaningful API(sequence of complex actions vs raw pixels)'''.<br />
<br />
= Introduction =<br />
<br />
Humans, frequently, use the ability to recover structured representation from raw sensation to understand their environment. Decomposing a picture of a hand-written character into strokes or understanding the layout of a building can be exploited to learn how actually our brain works. <br />
<br />
In the visual domain, inversion of a renderer for the purposes of scene understanding is typically referred to as inverse graphics. However, training vision systems using the inverse graphics approach has remained a challenge. Renderers typically expect as input programs that have sequential semantics, are composed of discrete symbols (e.g., keystrokes in a CAD program), and are long (tens or hundreds of symbols). Additionally, matching rendered images to real data poses an optimization problem as black-box graphics simulators are not differentiable in general. <br />
<br />
To address these problems, a new approach is presented for interpreting and generating images using Deep Reinforced Adversarial Learning in order to solve the need for a large amount of supervision and scalability to larger real-world datasets. In this approach, an adversarially trained agent '''(SPIRAL)''' generates a program which is executed by a graphics engine to generate images, either conditioned on data or unconditionally. The agent is rewarded by fooling a discriminator network and is trained with distributed reinforcement learning without any extra supervision. The discriminator network itself is trained to distinguish between generated and real images.<br />
<br />
[[File:Fig1 SPIRAL.PNG | 400px|center]]<br />
<br />
== Related Work ==<br />
Related works in this filed is summarized as follows:<br />
* There has been a huge amount of studies on inverting simulators to interpret images (Nair et al., 2008; Paysan et al., 2009; Mansinghka et al., 2013; Loper & Black, 2014; Kulkarni et al., 2015a; Jampani et al., 2015)<br />
<br />
* Inferring motor programs for reconstruction of MNIST digits (Nair & Hinton, 2006)<br />
<br />
* Visual program induction in the context of hand-written characters on the OMNIGLOT dataset (Lake et al., 2015)<br />
<br />
* inferring and learning feed-forward or recurrent procedures for image generation (LeCun et al., 2015; Hinton & Salakhutdinov, 2006; Goodfellow et al., 2014; Ackley et al., 1987; Kingma & Welling, 2013; Oord et al., 2016; Kulkarni et al., 2015b; Eslami et al., 2016; Reed et al., 2017; Gregor et al., 2015).<br />
<br />
'''However, all of these methods have limitations such as:''' <br />
<br />
* Scaling to larger real-world datasets<br />
<br />
* Requiring hand-crafted parses and supervision in the form of sketches and corresponding images<br />
<br />
* Lack the ability to infer structured representations of images<br />
<br />
= The SPIRAL Agent =<br />
=== Overview ===<br />
The paper aims to construct a generative model <math>\mathbf{G}</math> to take samples from a distribution <math>p_{d}</math>. The generative model consists of a recurrent network <math>\pi</math> (called policy network or agent) and an external rendering simulator R that accepts a sequence of commands from the agent and maps them into the domain of interest, e.g. R could be a CAD program rendering descriptions of primitives into 3D scenes. <br />
In order to train policy network <math>\pi</math>, the paper has exploited generative adversarial network. In this framework, the generator tries to fool a discriminator network which is trained to distinguish between real and fake samples. Thus, the distribution generated by <math>\mathbf{G}</math> approaches <math>p_d</math>.<br />
<br />
== Objectives ==<br />
The authors give training objective for <math>\mathbf{G}</math> and <math>\mathbf{D}</math> as follows.<br />
<br />
'''Discriminator:''' Following (Gulrajani et al., 2017), the objective for <math>\mathbf{D}</math> is defined as: <br />
<br />
\begin{align}<br />
\mathcal{L}_D = -\mathbb{E}_{x\sim p_d}[D(x)] + \mathbb{E}_{x\sim p_g}[D(x)] + R<br />
\end{align}<br />
<br />
where <math>\mathbf{R}</math> is a regularization term softly constraining <math>\mathbf{D}</math> to stay in the set of Lipschitz continuous functions (for some fixed Lipschitz constant).<br />
<br />
'''Generator:''' To define the objective for <math>\mathbf{G}</math>, a variant of the REINFORCE (Williams, 1992) algorithm, advantage actor-critic (A2C) is employed:<br />
<br />
<br />
\begin{align}<br />
\mathcal{L}_G = -\sum_{t}\log\pi(a_t|s_t;\theta)[R_t - V^{\pi}(s_t)]<br />
\end{align}<br />
<br />
<br />
where <math>V^{\pi}</math> is an approximation to the value function which is considered to be independent of theta, and <math>R_{t} = \sum_{t}^{N}r_{t}</math> is a <br />
1-sample Monte-Carlo estimate of the return. Rewards are set to:<br />
<br />
<math><br />
r_t = \begin{cases}<br />
0 & \text{for } t < N \\<br />
D(\mathcal{R}(a_1, a_2, \cdots, a_N)) & \text{for } t = N<br />
\end{cases}<br />
</math><br />
<br />
<br />
<br />
One interesting aspect of this new formulation is that <br />
the search can be biased by introducing intermediate rewards<br />
which may depend not only on the output of R but also on<br />
commands used to generate that output.<br />
<br />
== Conditional generation: ==<br />
In some cases such as producing a given image <math>x_{target}</math>, conditioning the model on auxiliary inputs is useful. That can be done by feeding <math>x_{target}</math> to both policy and discriminator networks as:<br />
<math><br />
p_g = R(p_a(a|x_{target}))<br />
</math><br />
<br />
While <math>p_{d}</math> becomes a Dirac-<math>\delta</math> function centered at <math>x_{target}</math>. <br />
For the first two terms in the objective function for D, they reduce to <br />
<math><br />
-D(x_{target}|x_{target})+ \mathbb{E}_{x\sim p_g}[D(x|x_{target})] <br />
</math><br />
<br />
It can be proven that for this particular setting of <math>p_{g}</math> and <math>p_{d}</math>, the <math>l2</math>-distance is an optimal discriminator. It may be as a poor candidate for the reward signal of the generator, even if it is not the only solution of the objective function for D.<br />
<br />
===Traditional GAN generation: ===<br />
Traditional GANs use the following minimax objective function to quantify optimality for relationships between D and G:<br />
<br />
[[File:edit7.png| 400px|center]]<br />
<br />
Minimizing the Jensen-Shannon divergence between the two distribution often leads to vanishing gradients as the discriminator saturates. We circumvent this issue using the conditional generation function, which is much better behaved.<br />
<br />
== Distributed Learning: ==<br />
The training pipeline is outlined in Figure 2b. It is an extension of the recently proposed '''IMPALA''' architecture (Espeholt et al., 2018). For training, three kinds of workers are defined:<br />
<br />
<br />
* Actors are responsible for generating the training trajectories through interaction between the policy network and the rendering simulator. Each trajectory contains a sequence <math>((\pi_{t}; a_{t}) | 1 \leq t \leq N)</math> as well as all intermediate<br />
renderings produced by R.<br />
<br />
<br />
* A policy learner receives trajectories from the actors, combines them into a batch and updates <math>\pi</math> by performing '''SGD''' step on <math>\mathcal{L}_G</math> (2). Following common practice (Mnih et al., 2016), <math>\mathcal{L}_G</math> is augmented with an entropy penalty encouraging exploration.<br />
<br />
<br />
* In contrast to the base '''IMPALA''' setup, an additional discriminator learner is defined. This worker consumes random examples from <math>p_{d}</math>, as well as generated data (final renders) coming from the actor workers, and optimizes <math>\mathcal{L}_D</math> (1).<br />
<br />
[[File:Fig2 SPIRAL Architecture.png | 700px|center]]<br />
<br />
'''Note:''' no trajectories are omitted in the policy learner. Instead, the <math>D</math> updates is decoupled from the <math>\pi</math> updates by introducing a replay buffer that serves as a communication layer between the actors and the discriminator learner. That allows the latter to optimize <math>D</math> at a higher rate than the training of the policy network due to the difference in network sizes (<math>\pi</math> is a multi-step RNN, while <math>D</math> is a plain '''CNN'''). Even though sampling from a replay buffer inevitably results in smoothing of <math>p_{g}</math>, this setup is found to work well in practice.<br />
<br />
= Experiments=<br />
<br />
<br />
== Environments ==<br />
Two rendering environment is introduced. For MNIST, OMNIGLOT and CELEBA generation an open-source painting librabry LIMBYPAINT (libmypaint<br />
contributors, 2018).) is used. The agent controls a brush and produces<br />
a sequence of (possibly disjoint) strokes on a canvas<br />
C. The state of the environment is comprised of the contents<br />
of <math>C</math> as well as the current brush location <math>l_{t}</math>. Each action<br />
<math>a_{t}</math> is a tuple of 8 discrete decisions <math>(a_t^1; a_t^2; ... ; a_t^8)</math> (see<br />
Figure 3). The first two components are the control point <math>p_{c}</math><br />
and the endpoint <math>l_{t+1}</math> of the stroke.<br />
<br />
[[File:Fig3_agent_action_space.PNG | 450px|center]]<br />
<br />
The next 5<br />
components represent the appearance of the stroke: the<br />
pressure that the agent applies to the brush (10 levels), the<br />
brush size, and the stroke color characterized by a mixture<br />
of red, green and blue (20 bins for each color component).<br />
The last element of at is a binary flag specifying the type<br />
of action: the agent can choose either to produce a stroke<br />
or to jump right to <math>l_{t+1}</math>.<br />
<br />
In the MUJOCO SCENES experiment, we render images<br />
using a MuJoCo-based environment (Todorov et al., 2012).<br />
At each time step, the agent has to decide on the object<br />
type (4 options), its location on a 16 <math>\times</math> 16 grid, its size<br />
(3 options) and the color (3 color components with 4 bins<br />
each). The resulting tuple is sent to the environment, which<br />
adds an object to the scene according to the specification.<br />
<br />
== Datasets ==<br />
<br />
=== MNIST ===<br />
For the MNIST dataset, two sets of experiments are conducted:<br />
<br />
1- In this experiment, an unconditional agent is trained to model the data distribution. Along with the reward provided by the discriminator, a small negative reward is provided to the agent for each continuous sequence of strokes to encourage the agent to draw a digit in a continuous motion of stroke. Example of such generation is depicted in the Fig 4a. <br />
<br />
2- In the second experiment, an agent is trained to reproduce a given digit. <br />
Several examples of conditional generated digits are shown in Fig 4b. <br />
<br />
[[File:Fig4a MNIST.png | 450px|center]]<br />
<br />
=== OMNIGLOT ===<br />
Now the trained agents are tested in a similar but more challenging setting of handwritten characters. As can be seen in Fig 5a, the unconditional generation has a lower quality compared to digits in the previous dataset. The conditional agents, on the other hand, were able to reach a convincing quality (Fig 5b). Moreover, as OMNIGLOT has lots of different symbols, the model that we created was able to learn a general idea of image production without memorizing the training data. We tested this result by inputting new unseen line drawings to our trained agent. As we concluded, it provided excellent results as shown in Figure 6. <br />
<br />
[[File:Fig5 OMNIGLOT.png | 450px|center]]<br />
<br />
<br />
For the MNIST dataset, two kinds of rewards, discriminator score and <math>l^{2}-\text{distance}</math> has been compared. Note that the discriminator based approach has a significantly lower training time and lower final <math>l^{2}</math> error.<br />
Following (Sharma et al., 2017), also a “blind” version of the agent without feeding any intermediate canvas states as an input to <math>\pi</math> is trained. The training curve for this experiment is also reported in Fig 8a. <br />
(dotted blue line) The results of training agents with discriminator based and <math>l^{2}-\text{distance}</math> approach is shown in Fig 8a as well.<br />
<br />
=== CELEBA ===<br />
<br />
Since the ''libmypaint'' environment is also capable of producing<br />
complex color paintings, this direction is explored by<br />
training a conditional agent on the CELEBA dataset. In this<br />
experiment, the agent does not receive any intermediate rewards.<br />
In addition to the reconstruction reward (either <math>l^2</math> or<br />
discriminator-based), earth mover’s<br />
distance between the color histograms of the model’s output<br />
and <math>x_{target}</math> is penalized. (Figure 7)<br />
<br />
[[File:Fig6 CELEBA.png | 450px|center]]<br />
<br />
Although blurry, the model’s reconstruction closely matches<br />
the high-level structure of each image such as the<br />
background color, the position of the face, and the color of<br />
the person’s hair. In some cases, shadows around eyes and<br />
the nose are visible.<br />
<br />
=== MUJOCO SCENES ===<br />
<br />
For the MUJOCO SCENES dataset, the trained agent is used to construct simple CAD programs that best explain input images. Here only the case of the conditional generation is considered. Like before, the reward function for the generator can be either the <math>l^2</math> score or the discriminator output. In addition, there are not any auxiliary reward signals. This model has the capacity to infer and represent up to 20 objects and their attributes due to its unrolled 20 time steps.<br />
<br />
As shown in Figure 8b, the agent trained to directly minimize<br />
<math>l^2</math> is unable to solve the task and has significantly<br />
higher pixel-wise error. In comparison, the discriminator based<br />
variant solves the task and produces near-perfect reconstructions<br />
on a holdout set (Figure 10).<br />
<br />
[[File:Fig8 MUJOCO_SCENES.png | 500px|center]]<br />
For this experiment, the total number of possible execution traces is <math>M^N</math>, where <math>M = 4·16^2·3·4^3·3 </math> is the total number of attribute settings for a single object and N = 20 is the length of an episode. Then a general-purpose Metropolis-Hastings inference algorithm that samples an execution trace defining attributes for a maximum of 20 primitives was run on a set of 100 images. These attributes are considered as latent variables. During each time step of the inference, the attribute blocks (including presence/absence tags) corresponding to a single object are evenly flipped over the appropriate range. The resulting trace is presented as an output sample by the environment and then the output sample is accepted or rejected using the Metropolis-Hastings update rule, where the Gaussian likelihood is centered on the test image and the fixed diagonal covariance is 0.25. From Figure 9, the MCMC search baseline cannot solve the task even after a lot of evaluation.<br />
[[File:figure9 mcmc.PNG| 500px|center]]<br />
<br />
= Discussion =<br />
As in the OMNIGLOT<br />
experiment, the <math>l^2</math>-based agent demonstrates some<br />
improvements over the random policy but gets stuck and as<br />
a result, fails to learn sensible reconstructions (Figure 8b).<br />
<br />
[[File:Fig7 Results.png | 500px|center]]<br />
<br />
<br />
Scaling visual program synthesis to the real world and combinatorial<br />
datasets has been a challenge. It has been shown that it is possible to train an adversarial generative agent employing<br />
black-box rendering simulator. Our results indicate that<br />
using the Wasserstein discriminator’s output as a reward<br />
function with asynchronous reinforcement learning can provide<br />
a scaling path for visual program synthesis. The current<br />
exploration strategy used in the agent is entropy-based but<br />
future work should address this limitation by employing sophisticated<br />
search algorithms for policy improvement. For<br />
instance, Monte Carlo Tree Search can be used, analogous<br />
to AlphaGo Zero (Silver et al., 2017). General-purpose<br />
inference algorithms could also be used for this purpose.<br />
<br />
= Critique and Future Work =<br />
* The architecture isn't new but it's a nice application and it's fun to watch the video of the robot painting in real life. SPIRAL's GAN-like idea continues the vein of [https://arxiv.org/abs/1610.01945 connecting actor-critic RL with GANs] like " [https://arxiv.org/abs/1706.03741Deep reinforcement learning from human preferences]" , Christiano et al 2017 or GAIL:<br />
<br />
* Future work should explore different parameterizations of action spaces. For instance, the use of two arbitrary control points are perhaps not the best way to represent strokes, as it is hard to deal with straight lines. Actions could also directly parametrize 3D surfaces, planes, and learned texture models to invert richer visual scenes. <br />
<br />
* A potential application can be in the field of medical images specifically to enhance and recolor histopathology slides for better detection. Also, image restoration problems could be addressed based on these approaches.<br />
<br />
* On the reward side, using a joint image-action discriminator similar to BiGAN/ALI (Donahue et al., 2016; Dumoulin et al., 2016) (in this case, the policy can be viewed as an encoder, while the renderer becomes a decoder) could result in a more meaningful learning signal, since D will be forced to focus on the semantics of the image.<br />
<br />
= Other Resources =<br />
#Code implementation [https://github.com/carpedm20/SPIRAL-tensorflow]<br />
<br />
= References =<br />
<br />
# Yaroslav Ganin, Tejas Kulkarni, Igor Babuschkin, S.M. Ali Eslami, Oriol Vinyals, [[https://arxiv.org/abs/1804.01118]].</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Synthesizing_Programs_for_Images_usingReinforced_Adversarial_Learning&diff=42257Synthesizing Programs for Images usingReinforced Adversarial Learning2018-12-04T18:52:00Z<p>A22ravi: /* Cririque and Future Work */</p>
<hr />
<div>'''Synthesizing Programs for Images using Reinforced Adversarial Learning: ''' Summary of the ICML 2018 paper <br />
<br />
Paper: [[http://proceedings.mlr.press/v80/ganin18a.html]]<br />
Video: [[https://www.youtube.com/watch?v=iSyvwAwa7vk&feature=youtu.be]]<br />
<br />
== Presented by ==<br />
<br />
1. Nekoei, Hadi [Quest ID: 20727088]<br />
<br />
= Motivation =<br />
<br />
Conventional neural generative models have major problems. <br />
<br />
* It is not clear how to inject knowledge about the data into the model. <br />
<br />
* Latent space is not easily interpretative. <br />
<br />
The provided solution in this paper is to generate programs to incorporate tools, e.g. graphics editors, illustration software, CAD. and '''creating more meaningful API(sequence of complex actions vs raw pixels)'''.<br />
<br />
= Introduction =<br />
<br />
Humans, frequently, use the ability to recover structured representation from raw sensation to understand their environment. Decomposing a picture of a hand-written character into strokes or understanding the layout of a building can be exploited to learn how actually our brain works. <br />
<br />
In the visual domain, inversion of a renderer for the purposes of scene understanding is typically referred to as inverse graphics. However, training vision systems using the inverse graphics approach has remained a challenge. Renderers typically expect as input programs that have sequential semantics, are composed of discrete symbols (e.g., keystrokes in a CAD program), and are long (tens or hundreds of symbols). Additionally, matching rendered images to real data poses an optimization problem as black-box graphics simulators are not differentiable in general. <br />
<br />
To address these problems, a new approach is presented for interpreting and generating images using Deep Reinforced Adversarial Learning in order to solve the need for a large amount of supervision and scalability to larger real-world datasets. In this approach, an adversarially trained agent '''(SPIRAL)''' generates a program which is executed by a graphics engine to generate images, either conditioned on data or unconditionally. The agent is rewarded by fooling a discriminator network and is trained with distributed reinforcement learning without any extra supervision. The discriminator network itself is trained to distinguish between generated and real images.<br />
<br />
[[File:Fig1 SPIRAL.PNG | 400px|center]]<br />
<br />
== Related Work ==<br />
Related works in this filed is summarized as follows:<br />
* There has been a huge amount of studies on inverting simulators to interpret images (Nair et al., 2008; Paysan et al., 2009; Mansinghka et al., 2013; Loper & Black, 2014; Kulkarni et al., 2015a; Jampani et al., 2015)<br />
<br />
* Inferring motor programs for reconstruction of MNIST digits (Nair & Hinton, 2006)<br />
<br />
* Visual program induction in the context of hand-written characters on the OMNIGLOT dataset (Lake et al., 2015)<br />
<br />
* inferring and learning feed-forward or recurrent procedures for image generation (LeCun et al., 2015; Hinton & Salakhutdinov, 2006; Goodfellow et al., 2014; Ackley et al., 1987; Kingma & Welling, 2013; Oord et al., 2016; Kulkarni et al., 2015b; Eslami et al., 2016; Reed et al., 2017; Gregor et al., 2015).<br />
<br />
'''However, all of these methods have limitations such as:''' <br />
<br />
* Scaling to larger real-world datasets<br />
<br />
* Requiring hand-crafted parses and supervision in the form of sketches and corresponding images<br />
<br />
* Lack the ability to infer structured representations of images<br />
<br />
= The SPIRAL Agent =<br />
=== Overview ===<br />
The paper aims to construct a generative model <math>\mathbf{G}</math> to take samples from a distribution <math>p_{d}</math>. The generative model consists of a recurrent network <math>\pi</math> (called policy network or agent) and an external rendering simulator R that accepts a sequence of commands from the agent and maps them into the domain of interest, e.g. R could be a CAD program rendering descriptions of primitives into 3D scenes. <br />
In order to train policy network <math>\pi</math>, the paper has exploited generative adversarial network. In this framework, the generator tries to fool a discriminator network which is trained to distinguish between real and fake samples. Thus, the distribution generated by <math>\mathbf{G}</math> approaches <math>p_d</math>.<br />
<br />
== Objectives ==<br />
The authors give training objective for <math>\mathbf{G}</math> and <math>\mathbf{D}</math> as follows.<br />
<br />
'''Discriminator:''' Following (Gulrajani et al., 2017), the objective for <math>\mathbf{D}</math> is defined as: <br />
<br />
\begin{align}<br />
\mathcal{L}_D = -\mathbb{E}_{x\sim p_d}[D(x)] + \mathbb{E}_{x\sim p_g}[D(x)] + R<br />
\end{align}<br />
<br />
where <math>\mathbf{R}</math> is a regularization term softly constraining <math>\mathbf{D}</math> to stay in the set of Lipschitz continuous functions (for some fixed Lipschitz constant).<br />
<br />
'''Generator:''' To define the objective for <math>\mathbf{G}</math>, a variant of the REINFORCE (Williams, 1992) algorithm, advantage actor-critic (A2C) is employed:<br />
<br />
<br />
\begin{align}<br />
\mathcal{L}_G = -\sum_{t}\log\pi(a_t|s_t;\theta)[R_t - V^{\pi}(s_t)]<br />
\end{align}<br />
<br />
<br />
where <math>V^{\pi}</math> is an approximation to the value function which is considered to be independent of theta, and <math>R_{t} = \sum_{t}^{N}r_{t}</math> is a <br />
1-sample Monte-Carlo estimate of the return. Rewards are set to:<br />
<br />
<math><br />
r_t = \begin{cases}<br />
0 & \text{for } t < N \\<br />
D(\mathcal{R}(a_1, a_2, \cdots, a_N)) & \text{for } t = N<br />
\end{cases}<br />
</math><br />
<br />
<br />
<br />
One interesting aspect of this new formulation is that <br />
the search can be biased by introducing intermediate rewards<br />
which may depend not only on the output of R but also on<br />
commands used to generate that output.<br />
<br />
== Conditional generation: ==<br />
In some cases such as producing a given image <math>x_{target}</math>, conditioning the model on auxiliary inputs is useful. That can be done by feeding <math>x_{target}</math> to both policy and discriminator networks as:<br />
<math><br />
p_g = R(p_a(a|x_{target}))<br />
</math><br />
<br />
While <math>p_{d}</math> becomes a Dirac-<math>\delta</math> function centered at <math>x_{target}</math>. <br />
For the first two terms in the objective function for D, they reduce to <br />
<math><br />
-D(x_{target}|x_{target})+ \mathbb{E}_{x\sim p_g}[D(x|x_{target})] <br />
</math><br />
<br />
It can be proven that for this particular setting of <math>p_{g}</math> and <math>p_{d}</math>, the <math>l2</math>-distance is an optimal discriminator. It may be as a poor candidate for the reward signal of the generator, even if it is not the only solution of the objective function for D.<br />
<br />
===Traditional GAN generation: ===<br />
Traditional GANs use the following minimax objective function to quantify optimality for relationships between D and G:<br />
<br />
[[File:edit7.png| 400px|center]]<br />
<br />
Minimizing the Jensen-Shannon divergence between the two distribution often leads to vanishing gradients as the discriminator saturates. We circumvent this issue using the conditional generation function, which is much better behaved.<br />
<br />
== Distributed Learning: ==<br />
The training pipeline is outlined in Figure 2b. It is an extension of the recently proposed '''IMPALA''' architecture (Espeholt et al., 2018). For training, three kinds of workers are defined:<br />
<br />
<br />
* Actors are responsible for generating the training trajectories through interaction between the policy network and the rendering simulator. Each trajectory contains a sequence <math>((\pi_{t}; a_{t}) | 1 \leq t \leq N)</math> as well as all intermediate<br />
renderings produced by R.<br />
<br />
<br />
* A policy learner receives trajectories from the actors, combines them into a batch and updates <math>\pi</math> by performing '''SGD''' step on <math>\mathcal{L}_G</math> (2). Following common practice (Mnih et al., 2016), <math>\mathcal{L}_G</math> is augmented with an entropy penalty encouraging exploration.<br />
<br />
<br />
* In contrast to the base '''IMPALA''' setup, an additional discriminator learner is defined. This worker consumes random examples from <math>p_{d}</math>, as well as generated data (final renders) coming from the actor workers, and optimizes <math>\mathcal{L}_D</math> (1).<br />
<br />
[[File:Fig2 SPIRAL Architecture.png | 700px|center]]<br />
<br />
'''Note:''' no trajectories are omitted in the policy learner. Instead, the <math>D</math> updates is decoupled from the <math>\pi</math> updates by introducing a replay buffer that serves as a communication layer between the actors and the discriminator learner. That allows the latter to optimize <math>D</math> at a higher rate than the training of the policy network due to the difference in network sizes (<math>\pi</math> is a multi-step RNN, while <math>D</math> is a plain '''CNN'''). Even though sampling from a replay buffer inevitably results in smoothing of <math>p_{g}</math>, this setup is found to work well in practice.<br />
<br />
= Experiments=<br />
<br />
<br />
== Environments ==<br />
Two rendering environment is introduced. For MNIST, OMNIGLOT and CELEBA generation an open-source painting librabry LIMBYPAINT (libmypaint<br />
contributors, 2018).) is used. The agent controls a brush and produces<br />
a sequence of (possibly disjoint) strokes on a canvas<br />
C. The state of the environment is comprised of the contents<br />
of <math>C</math> as well as the current brush location <math>l_{t}</math>. Each action<br />
<math>a_{t}</math> is a tuple of 8 discrete decisions <math>(a_t^1; a_t^2; ... ; a_t^8)</math> (see<br />
Figure 3). The first two components are the control point <math>p_{c}</math><br />
and the endpoint <math>l_{t+1}</math> of the stroke.<br />
<br />
[[File:Fig3_agent_action_space.PNG | 450px|center]]<br />
<br />
The next 5<br />
components represent the appearance of the stroke: the<br />
pressure that the agent applies to the brush (10 levels), the<br />
brush size, and the stroke color characterized by a mixture<br />
of red, green and blue (20 bins for each color component).<br />
The last element of at is a binary flag specifying the type<br />
of action: the agent can choose either to produce a stroke<br />
or to jump right to <math>l_{t+1}</math>.<br />
<br />
In the MUJOCO SCENES experiment, we render images<br />
using a MuJoCo-based environment (Todorov et al., 2012).<br />
At each time step, the agent has to decide on the object<br />
type (4 options), its location on a 16 <math>\times</math> 16 grid, its size<br />
(3 options) and the color (3 color components with 4 bins<br />
each). The resulting tuple is sent to the environment, which<br />
adds an object to the scene according to the specification.<br />
<br />
== Datasets ==<br />
<br />
=== MNIST ===<br />
For the MNIST dataset, two sets of experiments are conducted:<br />
<br />
1- In this experiment, an unconditional agent is trained to model the data distribution. Along with the reward provided by the discriminator, a small negative reward is provided to the agent for each continuous sequence of strokes to encourage the agent to draw a digit in a continuous motion of stroke. Example of such generation is depicted in the Fig 4a. <br />
<br />
2- In the second experiment, an agent is trained to reproduce a given digit. <br />
Several examples of conditional generated digits are shown in Fig 4b. <br />
<br />
[[File:Fig4a MNIST.png | 450px|center]]<br />
<br />
=== OMNIGLOT ===<br />
Now the trained agents are tested in a similar but more challenging setting of handwritten characters. As can be seen in Fig 5a, the unconditional generation has a lower quality compared to digits in the previous dataset. The conditional agents, on the other hand, were able to reach a convincing quality (Fig 5b). Moreover, as OMNIGLOT has lots of different symbols, the model that we created was able to learn a general idea of image production without memorizing the training data. We tested this result by inputting new unseen line drawings to our trained agent. As we concluded, it provided excellent results as shown in Figure 6. <br />
<br />
[[File:Fig5 OMNIGLOT.png | 450px|center]]<br />
<br />
<br />
For the MNIST dataset, two kinds of rewards, discriminator score and <math>l^{2}-\text{distance}</math> has been compared. Note that the discriminator based approach has a significantly lower training time and lower final <math>l^{2}</math> error.<br />
Following (Sharma et al., 2017), also a “blind” version of the agent without feeding any intermediate canvas states as an input to <math>\pi</math> is trained. The training curve for this experiment is also reported in Fig 8a. <br />
(dotted blue line) The results of training agents with discriminator based and <math>l^{2}-\text{distance}</math> approach is shown in Fig 8a as well.<br />
<br />
=== CELEBA ===<br />
<br />
Since the ''libmypaint'' environment is also capable of producing<br />
complex color paintings, this direction is explored by<br />
training a conditional agent on the CELEBA dataset. In this<br />
experiment, the agent does not receive any intermediate rewards.<br />
In addition to the reconstruction reward (either <math>l^2</math> or<br />
discriminator-based), earth mover’s<br />
distance between the color histograms of the model’s output<br />
and <math>x_{target}</math> is penalized. (Figure 7)<br />
<br />
[[File:Fig6 CELEBA.png | 450px|center]]<br />
<br />
Although blurry, the model’s reconstruction closely matches<br />
the high-level structure of each image such as the<br />
background color, the position of the face, and the color of<br />
the person’s hair. In some cases, shadows around eyes and<br />
the nose are visible.<br />
<br />
=== MUJOCO SCENES ===<br />
<br />
For the MUJOCO SCENES dataset, the trained agent is used to construct simple CAD programs that best explain input images. Here only the case of the conditional generation is considered. Like before, the reward function for the generator can be either the <math>l^2</math> score or the discriminator output. In addition, there are not any auxiliary reward signals. This model has the capacity to infer and represent up to 20 objects and their attributes due to its unrolled 20 time steps.<br />
<br />
As shown in Figure 8b, the agent trained to directly minimize<br />
<math>l^2</math> is unable to solve the task and has significantly<br />
higher pixel-wise error. In comparison, the discriminator based<br />
variant solves the task and produces near-perfect reconstructions<br />
on a holdout set (Figure 10).<br />
<br />
[[File:Fig8 MUJOCO_SCENES.png | 500px|center]]<br />
For this experiment, the total number of possible execution traces is <math>M^N</math>, where <math>M = 4·16^2·3·4^3·3 </math> is the total number of attribute settings for a single object and N = 20 is the length of an episode. Then a general-purpose Metropolis-Hastings inference algorithm that samples an execution trace defining attributes for a maximum of 20 primitives was run on a set of 100 images. These attributes are considered as latent variables. During each time step of the inference, the attribute blocks (including presence/absence tags) corresponding to a single object are evenly flipped over the appropriate range. The resulting trace is presented as an output sample by the environment and then the output sample is accepted or rejected using the Metropolis-Hastings update rule, where the Gaussian likelihood is centered on the test image and the fixed diagonal covariance is 0.25. From Figure 9, the MCMC search baseline cannot solve the task even after a lot of evaluation.<br />
[[File:figure9 mcmc.PNG| 500px|center]]<br />
<br />
= Discussion =<br />
As in the OMNIGLOT<br />
experiment, the <math>l^2</math>-based agent demonstrates some<br />
improvements over the random policy but gets stuck and as<br />
a result, fails to learn sensible reconstructions (Figure 8b).<br />
<br />
[[File:Fig7 Results.png | 500px|center]]<br />
<br />
<br />
Scaling visual program synthesis to the real world and combinatorial<br />
datasets has been a challenge. It has been shown that it is possible to train an adversarial generative agent employing<br />
black-box rendering simulator. Our results indicate that<br />
using the Wasserstein discriminator’s output as a reward<br />
function with asynchronous reinforcement learning can provide<br />
a scaling path for visual program synthesis. The current<br />
exploration strategy used in the agent is entropy-based but<br />
future work should address this limitation by employing sophisticated<br />
search algorithms for policy improvement. For<br />
instance, Monte Carlo Tree Search can be used, analogous<br />
to AlphaGo Zero (Silver et al., 2017). General-purpose<br />
inference algorithms could also be used for this purpose.<br />
<br />
= Critique and Future Work =<br />
* The architecture isn't new but it's a nice application and it's fun to watch the video of the robot painting in real life. SPIRAL's GAN-like idea continues the vein of [https://arxiv.org/abs/1610.01945 connecting actor-critic RL with GANs] like " [https://arxiv.org/abs/1706.03741Deep reinforcement learning from human preferences]" , Christiano et al 2017 or GAIL:<br />
<br />
* Future work should explore different parameterizations of action spaces. For instance, the use of two arbitrary control points are perhaps not the best way to represent strokes, as it is hard to deal with straight lines. Actions could also directly parametrize 3D surfaces, planes, and learned texture models to invert richer visual scenes. <br />
<br />
* On the reward side, using a joint image-action discriminator similar to BiGAN/ALI (Donahue et al., 2016; Dumoulin et al., 2016) (in this case, the policy can be viewed as an encoder, while the renderer becomes a decoder) could result in a more meaningful learning signal, since D will be forced to focus on the semantics of the image.<br />
<br />
= Other Resources =<br />
#Code implementation [https://github.com/carpedm20/SPIRAL-tensorflow]<br />
<br />
= References =<br />
<br />
# Yaroslav Ganin, Tejas Kulkarni, Igor Babuschkin, S.M. Ali Eslami, Oriol Vinyals, [[https://arxiv.org/abs/1804.01118]].</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=42256Annotating Object Instances with a Polygon RNN2018-12-04T18:35:33Z<p>A22ravi: /* Evaluation Metrics */</p>
<hr />
<div>Summary of the CVPR '17 best [https://www.cs.utoronto.ca/~fidler/papers/paper_polyrnn.pdf ''paper'']<br />
<br />
The presentation video of paper is available here[https://www.youtube.com/watch?v=S1UUR4FlJ84].<br />
<br />
= Background =<br />
<br />
If a snapshot of an image is given to a human, how will he/she describe a scene? He/she might identify that there is a car parked near the curb, or that the car is parked right beside a street light. This ability to decompose objects in scenes into separate entities is key to understanding what is around us and it helps to reason about the behavior of objects in the scene.<br />
<br />
Automating this process is a classic computer vision problem and is often termed "object detection". There are four distinct levels of detection (refer to Figure 1 for a visual cue):<br />
<br />
1. Classification + Localization: This is the most basic method that detects whether '''an''' object is either present or absent in the image and then identifies the position of the object within the image in the form of a bounding box overlayed on the image.<br />
<br />
2. Object Detection: The classic definition of object detection points to the detection and localization of '''multiple''' objects of interest in the image. The output of the detection is still a bounding box overlayed on the image at the position corresponding to the location of the objects in the image.<br />
<br />
3. Semantic Segmentation: This is a pixel level approach, i.e., each pixel in the image is assigned to a category label. Here, there is no difference between instances; this is to say that there are objects present from three distinct categories in the image, without tracking or reporting the number of appearances of each instance within a category. <br />
<br />
4. Instance Segmentation (''This paper performs this''): The goal is to not only to assign pixel-level categorical labels, but to identify each entity separately as sheep 1, sheep 2, sheep 3, grass, and so on.<br />
<br />
[[File:Figure_1.jpeg | 450px|thumb|center|Figure 1: Different levels of detection in an image.]]<br />
<br />
<br />
== Motivation ==<br />
<br />
Semantic segmentation helps us achieve a deeper understanding of images than image classification or object detection. Over and above this, instance segmentation is crucial in applications where multiple objects of the same category are to be tracked, especially in autonomous driving, mobile robotics, and medical image processing. This paper deals with a novel method to tackle the instance segmentation problem pertaining specifically to the field of autonomous driving, but shown to generalize well in other fields such as medical image processing.<br />
A polygon is natural form of annotation. Current instant segmentations annotated by humans use polygons because it is a special representation of the image which can use small number of vertices instead of various pixels and makes it easy to incorporate user modifications.<br />
<br />
[[File:polygon.png|600px|center]]<br />
<br />
== Goal ==<br />
<br />
Most of the recent approaches to on instance segmentation are based on deep neural networks and have demonstrated impressive performance. Given that these approaches require a lot of computational resources and that their performance depends on the amount of accessible training data, there has been an increase in the demand to label/annotate large-scale datasets. This is both expensive and time-consuming. <br />
<br />
{| class=wikitable width=700 align=center<br />
|Thus, the '''main goal''' of the paper is to enable '''semi-automatic''' annotation of object instances.<br />
|}<br />
<br />
Figure 2 demonstrates how the interface looks like for better clarity.<br />
<br />
Most of the datasets available pass through a stage where annotators manually outline the objects with a closed polygon. Polygons allow annotation of objects with a small number of clicks (30 - 40) compared to other methods. This approach works as the silhouette of an object is typically connected without holes. <br />
<br />
{| class=wikitable width=900 align=center<br />
|Thus, the authors suggest to adopt this same technique to annotate images using polygons, except they plan to automate the method and replace/reduce manual labeling. The '''intuition''' behind the success of this method is the '''sparse''' nature of these polygons that allow annotating of an object through a cluster of pixels rather than classification at the pixel-level.<br />
|}<br />
<br />
[[File:Annotating Object Instances Example.png | 450px|thumb|center|Figure 2: Given a bounding box, polygon outlining the the object instance inside the box is predicted. This approach is designed to facilitation annotation, and easily incorporates user corrections of points to improve the overall object’s polygon. ]]<br />
<br />
<br />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': In general, GrabCut is a method to separate the foreground and background of an image with minimal user interaction. Specifically, the user need only create a rectangular bounding box containing the foreground, and the algorithm will extract the object in the foreground. A major contribution of the paper is that labelling (of the object in the foreground) was not required, as the algorithm was able to identify where significant changes in colour pattern occurred. In this sense, it mimics automatic segmentation when combined with a Region Proposal Network. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 3: Illustration of GrabCut.]]<br />
<br />
2. '''GrabCut + CNN''': Scribbles have also been used to train CNNs for semantic image segmentation. <br />
<br />
3. '''Superpixels''': Superpixels in the form of small polygons where the color intensity within each superpixel is similar, to a certain threshold, have been used to provide a sparse representation of the large number of pixels in an image. However, the performance of this technique depends on the scale of the superpixels and hence sometimes merges small objects.<br />
<br />
[[File:Superpixel_idea.jpg | 450px|thumb|center|Figure 4: Illustration of the superpixel idea.]]<br />
<br />
= Model =<br />
<br />
As an '''input''' to the model, an annotator or perhaps another neural network provides a bounding box containing an object of interest and the model auto-generates a polygon outlining the object instance using a Recurrent Neural Network which they call: Polygon-RNN.<br />
<br />
The RNN model predicts the vertices of the polygon at each time step given a CNN representation of the image, the last two time steps, and the first vertex location. The location of the first vertex is defined differently and will be defined shortly. The information regarding the previous two-time steps helps the RNN create a polygon in a specific direction and the first vertex provides a cue for loop closure of the polygon edges.<br />
<br />
The polygon is parametrized as a sequence of 2D vertices and it is assumed that the polygon is closed. In addition, the polygon generation is fixed to follow a clockwise orientation since there are multiple ways to create a polygon given that it is cyclic structure. However, the starting point of the sequence is defined so that it can be any of the vertices of the polygon.<br />
<br />
== Architecture ==<br />
<br />
There are two primary networks at play: 1. CNN with skip connections, and 2. One-to-many type RNN.<br />
<br />
[[File:Figure_2_Neel.JPG | 800px|thumb|center|Figure 5: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type) ('''Note''': A possible point of confusion - the authors have only shown the layers of VGG16 architecture here that have the skip connections introduced).]]<br />
<br />
1. '''CNN with skip connections''':<br />
<br />
The authors have adopted the VGG16 feature extractor architecture with a few modifications pertaining to the preservation of features fused together in a tensor that can feed into the RNN (refer to Figure 5). Namely, the last max-pooling layer (''pool5'') present in the VGG16 CNN has been removed. The image fed into the CNN is pre-shrunk to a 224x224x3 tensor(3 being the Red, Green, and Blue channels). The image passes through 2 pooling layers and 2 convolutional layers. Since, the features extracted after each operation are to be preserved and fused later on, at each of these four steps, the idea is to have a tensor with a common width of 512; so the output tensor at pool2 is convolved with 4 3x3x128 filters and the output tensor at pool3 is convolved with 2 3x3x256 filters. The skip connections from the four layers allow the CNN to extract low-level edge and corner features (helps to follow the object's boundaries) as well as boundary/semantic information about the instances (helps to identify the object). Finally, a 3x3 convolution applied along with a ReLU non-linearity results in a 28x28x128 tensor that contains semantic information pertinent to the image frame and is taken as an input by the RNN.<br />
<br />
2. '''RNN - 2 Layer ConvLSTM'''<br />
<br />
The RNN is employed to capture information about the previous vertices in the time-series. Specifically, a Convolutional LSTM is used as a decoder. The ConvLSTM allows preservation of the spatial information in 2D received from CNN and reduces the number of parameters compared to a Fully Connected RNN. The polygon is modeled with a kernel size of 3x3 and 16 channels outputting a vertex at each time step. The ConvLSTM gets as input a tensor step t which<br />
concatenates 4 features: the CNN feature representation of the image, one-hot encoding of the previous predicted vertex and the vertex predicted<br />
from two time steps ago, as well as the one-hot encoding of the first predicted vertex. <br />
<br />
The Convolutional LSTM computes the hidden state <math display = "inline">h_t</math> given the input <math display = "inline">x_t</math> based on the following equations:<br />
<center><br />
<math display="block"><br />
\begin{pmatrix}<br />
i_t \\<br />
f_t \\<br />
o_t \\<br />
g_t \\<br />
\end{pmatrix}<br />
= W_h * h_{t-1} + W_x * x_t + b<br />
</math><br />
<br />
<math display="block"><br />
c_t = \sigma(f_t) \bigodot c_{t-1} + \sigma(i_t) \bigodot tanh(g_t)<br />
</math><br />
<br />
<math display="block"><br />
h_t = \sigma(o_t) \bigodot tanh(c_t)<br />
</math><br />
</center><br />
where <math display = "inline">i, f, o</math> denote the input, forget, and output gate, <math display = "inline">h</math> is the hidden state and <math display = "inline">c</math> is the cell state. Also, <math display = "inline">\sigma</math> denotes the sigmoid function, <math display = "inline">\bigodot</math> indicates an element-wise product and <math display = "inline">*</math> a convolution. <math display = "inline">W_h</math> denotes the hidden-to-state convolution kernel and <math display = "inline">W_x</math> the input-to-state convolution kernel.<br />
<br />
The authors have treated the vertex prediction task as a classification task in that the location of the vertices is through a one-hot representation of dimension DxD + 1 (D chosen to be 28 by the authors in tests). The one additional dimension is the storage cue for loop closure for the polygon. Given that, the one-hot representation of the two previously predicted vertices and the first vertex are taken in as an input, a clockwise (or for that reason any fixed direction) direction can be forced for the creation of the polygon. Coming back to the prediction of the first vertex, as polygon is a circle, any vertex of a polygon can be used as a starting point. Therefore the authors treat the starting point as special, and this is done through further modification of the CNN by adding two DxD layers with one branch predicting object instance boundaries while the other takes in this output as well as the image features to predict vertices of the polygon. The boundaries and vertices prediction are being treated as binary classification problem in each cell in the output grid. This CNN is trained separately. Here, <math display = "inline">y_t</math> denotes the one-hot encoding of the vertex and is the output at time step <math>t</math>.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN loss function. To avoid over-penalizing of mispredictions that are close to the ground-truth vertex, non-zero probability mass are assigned to locations which are within a distance of 2 in D × D output grid.<br />
<br />
2. The typical training regime, where the model make predictions at each time step but feed in ground-truth vertex information to the next, is followed. Instead of Stochastic Gradient Descent, Adam is used for optimization: batch size = 8, learning rate = 1e^-4 (learning rate decays after 10 epochs by a factor of 10) This choice of optimizer makes it easier for development, but switching back to SGD may get better experimental results due to convergence problems of Adam.<br />
<br />
3. For the first vertex prediction, the modified CNN mentioned previously, is trained using a multi-task cost function. In particular, the authors used the logistic loss for every location in the grid.<br />
<br />
The reported time for training is one day on a Nvidia Titan-X GPU.<br />
<br />
The resolution of the polygon is 28 x 28, based on the downsampling factor and ConvLSTM resolution. They simplified the polygon by removing vertices on the grid line and the same vertices that fall in the same grid. They also randomly flipped images, enlarged original bounding boxes and randomly selected the starting vertex of the polygon notation as their data augmentation process.<br />
<br />
== Importance of Human Annotator in the Loop ==<br />
<br />
The model allows for the prediction at a given time step to be corrected and this corrected vertex is then fed into the next time step of the RNN, effectively rejecting the network predicted vertex. This has the simple effect of putting the model "back on the right track". Note that this is only possible due to the adoption of the RNN architecture i.e. the inherent nature of the RNN to accept previous outputs allows incorporation of the user's judgement. The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
== Evaluation Metrics ==<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. There are two metrics used for evaluation:<br />
<br />
1. '''IoU''': The standard Intersection over Union (IoU) measure is used for comparison. In add The calculation for IoU takes both the predicted and ground-truth object boundaries. The intersection (area contained in both boundaries at once) is divided by the union (the area contained by at least one, or both, of the boundaries). A low score of this metric would mean that there is little overlap between the boundaries, or large areas on non-overlap, and a score of 1.0 would indicate that the two boundaries contain the same area.<br />
<br />
An example of the IoU is illustrated in the figure below:<br />
<br />
[[File:IoU_figure.png|500px|center]] Source:https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/<br />
<br />
2. '''Number of Clicks''': To evaluate the speed up factor, the checkerboard distance is used to measure the distance between the ground truth (GT) and the output of the Polygon RNN. A set of distance thresholds are set <math display = "inline">T &isin; [1,2,3,4]</math> and if the distance exceeds the particular threshold, the correction is made by an annotator to match the GT and the '''Number of Clicks''' is used to evaluate the speed up factor.<br />
<br />
== Baseline Techniques ==<br />
<br />
1. '''SharpMask''': a 50 layer ResNet considered as the state of the art annotation method.<br />
<br />
2. '''DeepMask''': a build-up on the 50 layer ResNet with an addition of another CNN.<br />
<br />
3. '''Dilation10''': another simple technique using purely convolutional operations.<br />
<br />
4. '''SquareBox''': a simple technique where an entire bounding box is labeled as an object<br />
<br />
== Quantitative Results ==<br />
<br />
We report the IoU metric in Table<br />
1. The Polygon RNN method outperforms the baselines in 6 out of the 8 categories and has a mean IoU greater than all of the baselines. Particularly, in the car, person, and rider categories, a 12%, 7%, and 6% higher performance than SharpMask is achieved.<br />
<br />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
In addition, with the help of the annotator, the speedup factor was 7.3 times with under 5 clicks which the authors claim is the main advantage of this method.<br />
<br />
[[File:Table_0_Neel.JPG | 800px|thumb|center|Table 2: IoU performance on Cityscapes data with annotator intervention.]]<br />
<br />
The method also works well with other datasets such as KITTI:<br />
<br />
[[File:Table_2_Neel.JPG | 800px|thumb|center|Table 3: IoU performance on KITTI data.]]<br />
<br />
== Effect of object size ==<br />
In Fig. 4, we see how our model performs w.r.t baselines on different instance sizes. For small instances, our model performs significantly better than the baselines. For larger objects, the baselines have an advantage due to the larger output resolution. <br />
<br />
[[File:IoU_vs_size_of_instance.PNG | 500px|thumb|center|Fig 4: IoU_vs_size_of_instance.]]<br />
<br />
== Qualitative Results ==<br />
<br />
In addition, most of the comparisons with human annotators show that the method is at par with human-level annotation.<br />
<br />
<gallery widths=500px heights=500px perrow=2 mode="packed"><br />
File:Figure_3_Neel.JPG|Figure 6: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 7: Qualitative results: comparison with human annotator.|alt=alt language<br />
</gallery><br />
<br />
=Conclusion=<br />
<br />
The important conclusions from this paper are:<br />
<br />
1. The paper presented a powerful generic annotation tool for modelling complex annotations as a simple polygon that works on different unseen datasets. <br />
<br />
2. Significant improvement in annotation time can be achieved with the Polygon-RNN method itself (speed-up factor of 4.74).<br />
<br />
3. However, the flexibility of having inputs from a human annotator helps increase the IoU for a certain range of clicks.<br />
<br />
4. The model architecture has a down-sampling factor of 16 and the final output resolution and accuracy is sensitive to object size.<br />
<br />
5. Another downside of the model architecture is that training time is increased due to the training of the CNN for the first vertex.<br />
<br />
=Critique=<br />
<br />
1. With the human annotator in the loop, the model speeds up the process of annotation by over 7 times which is perhaps a big cost and time cutting improvement for companies.<br />
<br />
2. Given that this model uses the VGG16 architecture compared to the 50 layer ResNet in SharpMask, this method is quite efficient.<br />
<br />
3. This paper requires training of an entire CNN for the first vertex and is inefficient in that sense as it introduces additional parameters adding to the computation time and resource demand.<br />
<br />
4. The baseline methods have an upper hand compared to this model when it comes to larger objects since the nature of the down-scaled structure adopted by this model.<br />
<br />
5. In terms of future work, elimination of the additional CNN for the first vertex as well as an enhanced architecture to remain insensitive to the size of the object to be annotated should be implemented.<br />
<br />
6. Compared to other models, the model was shown to not perform as well for larger objects (see table 3). This is likely due to the fact that vertex location determination is done in a highly compressed (28x28) representation compared to the input image(224x224). For larger objects, bounding boxes are larger. Each vertex represents many pixels. When up-converted back to the input image/bounding box size these may lead to errors especially when considering a very precise evaluation metric (intersection over union) is used. Potentially, the results can be improved by considering a higher resolution for the internal representation or one that scales with the size of the bounding.<br />
<br />
7. While the model outperforms the baseline for certain categories of object, it is surprising that it underperforms in categories such as 'bus' and 'train'. With human annotators in the loop, one would expect the model to outperform in all categories.<br />
<br />
8. One of the major contributions of this paper lies on the fact that this paper presents a method that does have an applicable value in the real world. In the paper, it does show that it can greatly reduce the human labeling efforts, and with human collaboration, this algorithm can help us tackle the image labeling problem much more efficiently. However, it does not provide the theoretical explanation that why would an RNN work better than a CNN in this case, a more in-depth analysis would make the paper better.<br />
<br />
=Code=<br />
# [https://github.com/AlexMa011/pytorch-polygon-rnn] (unofficial)<br />
# Code for an updated version of the model is available at [https://github.com/fidler-lab/polyrnn-pp] (official)</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:IoU_figure.png&diff=42255File:IoU figure.png2018-12-04T18:33:49Z<p>A22ravi: </p>
<hr />
<div></div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=42245Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-12-03T07:10:01Z<p>A22ravi: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search (NAS) has emerged, which is to automatically find an optimal neural architecture for a given task in a well-defined architecture space. The resulting architectures have often outperform networks designed by human experts on tasks such as image classification and natural language processing. [2,3,4] <br />
<br />
This paper presents a meta-learning technique to have computers search for a neural architecture that performs well on the task of dense image segmentation, mainly focused on the problem of scene labeling.<br />
<br />
=Motivation=<br />
<br />
The part of deep neural networks(DNN) success is largely due to the fact that it greatly reduces the work in feature engineering. This is because DNNs have the ability to extract useful features given the raw input. However, this creates a new paradigm to look at - network engineering. In order to extract significant features, an appropriate network architecture must be used. Hence, the engineering work is shifted from feature engineering to network architecture design for better abstraction of features.<br />
<br />
The motivation for NAS is to establish a guiding theory behind how to design the optimal network architecture. Given that there is an <br />
abundant amount of computational resources available, an intuitive solution is to define a finite search space for a computer to search for optimal network structures and hyperparameters.<br />
<br />
=Related Work =<br />
<br />
This paper focuses on two main literature research topics. One is the neural architecture search (NAS) and the other is the Multi-Scale representation for dense image prediction. Neural architecture search trains a controller network to generate neural architectures. The following are the important research directions in this area: <br />
<br />
1) One kind of research transfers architectures learned on a proxy dataset to more challenging datasets and demonstrates superior performance over many human-invented architectures.<br />
<br />
2) Reinforcement learning, evolutionary algorithms and sequential model-based optimization have been used to learn network structures. <br />
<br />
3) Some other works focus on increasing model size, sharing model weights to accelerate model search or a continuous relaxation of the architecture representation. <br />
<br />
4) Some recent methods focus on proposing methods for embedding an exponentially large number of architectures in a grid arrangement for semantic segmentation tasks. <br />
<br />
In the area of multi-scale representation for dense image prediction the following are useful prior work: <br />
<br />
1) State of the art methods use Convolutional Neural Nets. There are different methods proposed for supplying global features and context information to perform pixel level classification. <br />
<br />
2) Some approaches focus on how to efficiently encode multi-scale context information in a network architecture like designing models that take an input an image pyramid so that large-scale objects are captured by the downsampled image. <br />
<br />
3) Research also tried to come up with a theme on how best to tune the architecture to extract context information. Some works focus on sampling rates in atrous convolution to encode multi-scale context. Some others build context module by gradually increasing the rate on top of belief maps.<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol><br />
The search space is easy to understand, for instance defining a hyperparameter space to consider for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumptions we make on the neural architecture. The search strategy details how to explore the search space. The evaluation strategy refers to taking an input of a set of hyperparameters, and from there evaluating how well our model fits. In the field of NAS, it is typical to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
The purpose of architecture search space is to design a space that can express various state-of-the-art architectures, and able to identify good models.<br />
<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|150px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|400px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|600px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC" which represented by a directed acyclic graph (DAG) with five branches (i.e. the optimal value, which gives a good balance between flexibility and computational tractability). A DAG is a finite directed graph with no directed cycles which consists of finitely many vertices and edges, with each edge directed from one vertex to another, such that there is no way to start at any vertex <math>v</math> and follow a consistently-directed sequence of edges that eventually loops back to <math>v</math> again. The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell, that is a recursive search space to encode multi-scale context information for dense prediction tasks. In theory, the search space consists of what they choose for the network backbone and the internal structure of the DPC. In practice, they just used MobileNet and Modified Xception net as the backbone. So the search space only consists of the internal structure of the DPC cell.<br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
For the spatial pyramid pooling operation, average pooling is performed in each grid. After the<br />
average pooling, a 1×1 convolution is applied and the then the resize back the features to have the same spatial resolution as the input tensor.<br />
<br />
Separable convolution with 256 filters is employed for all convolutions and 3x3 atrous convolutions with sampling rates rh x rw allows for capturing object scales with different aspect ratios. This is illustrated in the diagram below: <br />
<br />
[[File:NAS_fig2.png|center|500px]]<br />
<br />
Average spatial pyramid pooling is performs mean pooling on the last convolution layer (either convolution or sub sampling) and produces a N*B dimensional vector (where N=Number of filters in the convolution layer, B= Number of Bins). The vector is in turn fed to the fully connected layer. The number of bins is a constant value. Therefore, the vector dimension remains constant irrespective of the input image size.<br />
<br />
The resulting search space is able to encode all the main state-of-the-art architectures(i.e. Deformable Convnets [11], ASPP, Dense-ASPP [12] etc.), but these encoded architectures are more diverse since each branch of a DPC cell could build contextual information through parallel or cascaded representations. The number of potential architectures may determine the potential diversity of the search space. For <math display="inline">i</math>-th branch, there are <math display="inline">i</math> possible inputs, including the last feature maps produced by the network backbone, all the outputs from previous branch (<math display="inline">i.e., Y_1,...,Y_{i-1}</math>), and also 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in <math display="inline">i × 81</math> possible options. Therefore, for B = 5, the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|600px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
The pseudocode for a general random search algorithm is provided below.<br />
<br />
[[File:Pseudoc.png |700px|center]]<br />
<br />
It essentially repeatedly searches randomly within the hypersphere of the current state, and updates only if the reward function is increased when using the newly found vector. The approach is highly non-parametric, and is easily generalized for complex problems such as architectural finding once parameters are properly defined. Although Random Search can return a reasonable approximation of the optimal solution under low problem dimensionality, the approach is commonly cited to perform poorly under higher problem dimensionality. The implementation of Random Search within this context is used to find highly complex architectures with millions of parameters; this could explain the only marginal improvements to human created state-of-the art networks despite the heavy machinery used to arrive at new architectures in the experiments section.<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques [7]. In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]. A more recent and detailed survey detailing other methods such as Bayesian optimization strategies for Neural architecture search can be found in [13]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 800px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|1000px]]<br />
</div><br />
<br />
Table 2 describes the results on scene parsing dataset. It sets a new state-of-the-art performance of 82.7% mIOU and outperforms other state-of-the-art models across 11 of the 19 categories.<br />
<br />
Table 3 describes the results on person part segmentation dataset. It achieve the state-of-the-art performance of 71.34% mIOU and outperforms other state-of-the-art models across 6 of the 7 categories.<br />
<br />
Table 4 describes the results on semantic image segmentation dataset. It achieve the state-of-the-art performance of 87.9% mIOU and outperforms other state-of-the-art models across 6 of the 20 categories.<br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy. They hope that by using some meta learning on metadata it can lead to future insight and be advantageous. <br />
<br />
The author hope that this architecture search techniques can be ported into other domains such as depth prediction and object detection to achieve similar gains over human-invented designs.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
11. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei. Deformable convolutional networks. In ICCV, 2017.<br />
<br />
12. M. Yang, K. Yu, C. Zhang, Z. Li, and K. Yang. Denseaspp for semantic segmentation in street scenes. In CVPR, 2018.<br />
<br />
13. Elsken, Thomas, Jan Hendrik Metzen, and Frank Hutter. "Neural architecture search: A survey." arXiv preprint arXiv:1808.05377 (2018).</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=42244Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-12-03T07:09:25Z<p>A22ravi: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search (NAS) has emerged, which is to automatically find an optimal neural architecture for a given task in a well-defined architecture space. The resulting architectures have often outperform networks designed by human experts on tasks such as image classification and natural language processing. [2,3,4] <br />
<br />
This paper presents a meta-learning technique to have computers search for a neural architecture that performs well on the task of dense image segmentation, mainly focused on the problem of scene labeling.<br />
<br />
=Motivation=<br />
<br />
The part of deep neural networks(DNN) success is largely due to the fact that it greatly reduces the work in feature engineering. This is because DNNs have the ability to extract useful features given the raw input. However, this creates a new paradigm to look at - network engineering. In order to extract significant features, an appropriate network architecture must be used. Hence, the engineering work is shifted from feature engineering to network architecture design for better abstraction of features.<br />
<br />
The motivation for NAS is to establish a guiding theory behind how to design the optimal network architecture. Given that there is an <br />
abundant amount of computational resources available, an intuitive solution is to define a finite search space for a computer to search for optimal network structures and hyperparameters.<br />
<br />
=Related Work =<br />
<br />
This paper focuses on two main literature research topics. One is the neural architecture search (NAS) and the other is the Multi-Scale representation for dense image prediction. Neural architecture search trains a controller network to generate neural architectures. The following are the important research directions in this area: <br />
<br />
1) One kind of research transfers architectures learned on a proxy dataset to more challenging datasets and demonstrates superior performance over many human-invented architectures.<br />
<br />
2) Reinforcement learning, evolutionary algorithms and sequential model-based optimization have been used to learn network structures. <br />
<br />
3) Some other works focus on increasing model size, sharing model weights to accelerate model search or a continuous relaxation of the architecture representation. <br />
<br />
4) Some recent methods focus on proposing methods for embedding an exponentially large number of architectures in a grid arrangement for semantic segmentation tasks. <br />
<br />
In the area of multi-scale representation for dense image prediction the following are useful prior work: <br />
<br />
1) State of the art methods use Convolutional Neural Nets. There are different methods proposed for supplying global features and context information to perform pixel level classification. <br />
<br />
2) Some approaches focus on how to efficiently encode multi-scale context information in a network architecture like designing models that take an input an image pyramid so that large-scale objects are captured by the downsampled image. <br />
<br />
3) Research also tried to come up with a theme on how best to tune the architecture to extract context information. Some works focus on sampling rates in atrous convolution to encode multi-scale context. Some others build context module by gradually increasing the rate on top of belief maps.<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol><br />
The search space is easy to understand, for instance defining a hyperparameter space to consider for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumptions we make on the neural architecture. The search strategy details how to explore the search space. The evaluation strategy refers to taking an input of a set of hyperparameters, and from there evaluating how well our model fits. In the field of NAS, it is typical to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
The purpose of architecture search space is to design a space that can express various state-of-the-art architectures, and able to identify good models.<br />
<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|150px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|400px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|600px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC" which represented by a directed acyclic graph (DAG) with five branches (i.e. the optimal value, which gives a good balance between flexibility and computational tractability). A DAG is a finite directed graph with no directed cycles which consists of finitely many vertices and edges, with each edge directed from one vertex to another, such that there is no way to start at any vertex <math>v</math> and follow a consistently-directed sequence of edges that eventually loops back to <math>v</math> again. The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell, that is a recursive search space to encode multi-scale context information for dense prediction tasks. In theory, the search space consists of what they choose for the network backbone and the internal structure of the DPC. In practice, they just used MobileNet and Modified Xception net as the backbone. So the search space only consists of the internal structure of the DPC cell.<br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
For the spatial pyramid pooling operation, average pooling is performed in each grid. After the<br />
average pooling, a 1×1 convolution is applied and the then the resize back the features to have the same spatial resolution as the input tensor.<br />
<br />
Separable convolution with 256 filters is employed for all convolutions and 3x3 atrous convolutions with sampling rates rh x rw allows for capturing object scales with different aspect ratios. This is illustrated in the diagram below: <br />
<br />
[[File:NAS_fig2.png|center|500px]]<br />
<br />
Average spatial pyramid pooling is performs mean pooling on the last convolution layer (either convolution or sub sampling) and produces a N*B dimensional vector (where N=Number of filters in the convolution layer, B= Number of Bins). The vector is in turn fed to the fully connected layer. The number of bins is a constant value. Therefore, the vector dimension remains constant irrespective of the input image size.<br />
<br />
The resulting search space is able to encode all the main state-of-the-art architectures(i.e. Deformable Convnets [11], ASPP, Dense-ASPP [12] etc.), but these encoded architectures are more diverse since each branch of a DPC cell could build contextual information through parallel or cascaded representations. The number of potential architectures may determine the potential diversity of the search space. For <math display="inline">i</math>-th branch, there are <math display="inline">i</math> possible inputs, including the last feature maps produced by the network backbone, all the outputs from previous branch (<math display="inline">i.e., Y_1,...,Y_{i-1}</math>), and also 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in <math display="inline">i × 81</math> possible options. Therefore, for B = 5, the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|600px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
The pseudocode for a general random search algorithm is provided below.<br />
<br />
[[File:Pseudoc.png |700px|center]]<br />
<br />
It essentially repeatedly searches randomly within the hypersphere of the current state, and updates only if the reward function is increased when using the newly found vector. The approach is highly non-parametric, and is easily generalized for complex problems such as architectural finding once parameters are properly defined. Although Random Search can return a reasonable approximation of the optimal solution under low problem dimensionality, the approach is commonly cited to perform poorly under higher problem dimensionality. The implementation of Random Search within this context is used to find highly complex architectures with millions of parameters; this could explain the only marginal improvements to human created state-of-the art networks despite the heavy machinery used to arrive at new architectures in the experiments section.<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
A more recent and detailed survey detailing other methods such as Bayesian optimization strategies for Neural architecture search can be found in [13]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 800px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|1000px]]<br />
</div><br />
<br />
Table 2 describes the results on scene parsing dataset. It sets a new state-of-the-art performance of 82.7% mIOU and outperforms other state-of-the-art models across 11 of the 19 categories.<br />
<br />
Table 3 describes the results on person part segmentation dataset. It achieve the state-of-the-art performance of 71.34% mIOU and outperforms other state-of-the-art models across 6 of the 7 categories.<br />
<br />
Table 4 describes the results on semantic image segmentation dataset. It achieve the state-of-the-art performance of 87.9% mIOU and outperforms other state-of-the-art models across 6 of the 20 categories.<br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy. They hope that by using some meta learning on metadata it can lead to future insight and be advantageous. <br />
<br />
The author hope that this architecture search techniques can be ported into other domains such as depth prediction and object detection to achieve similar gains over human-invented designs.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
11. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei. Deformable convolutional networks. In ICCV, 2017.<br />
<br />
12. M. Yang, K. Yu, C. Zhang, Z. Li, and K. Yang. Denseaspp for semantic segmentation in street scenes. In CVPR, 2018.<br />
<br />
13. Elsken, Thomas, Jan Hendrik Metzen, and Frank Hutter. "Neural architecture search: A survey." arXiv preprint arXiv:1808.05377 (2018).</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=42243Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-12-03T07:08:02Z<p>A22ravi: /* References */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search (NAS) has emerged, which is to automatically find an optimal neural architecture for a given task in a well-defined architecture space. The resulting architectures have often outperform networks designed by human experts on tasks such as image classification and natural language processing. [2,3,4] <br />
<br />
This paper presents a meta-learning technique to have computers search for a neural architecture that performs well on the task of dense image segmentation, mainly focused on the problem of scene labeling.<br />
<br />
=Motivation=<br />
<br />
The part of deep neural networks(DNN) success is largely due to the fact that it greatly reduces the work in feature engineering. This is because DNNs have the ability to extract useful features given the raw input. However, this creates a new paradigm to look at - network engineering. In order to extract significant features, an appropriate network architecture must be used. Hence, the engineering work is shifted from feature engineering to network architecture design for better abstraction of features.<br />
<br />
The motivation for NAS is to establish a guiding theory behind how to design the optimal network architecture. Given that there is an <br />
abundant amount of computational resources available, an intuitive solution is to define a finite search space for a computer to search for optimal network structures and hyperparameters.<br />
<br />
=Related Work =<br />
<br />
This paper focuses on two main literature research topics. One is the neural architecture search (NAS) and the other is the Multi-Scale representation for dense image prediction. Neural architecture search trains a controller network to generate neural architectures. The following are the important research directions in this area: <br />
<br />
1) One kind of research transfers architectures learned on a proxy dataset to more challenging datasets and demonstrates superior performance over many human-invented architectures.<br />
<br />
2) Reinforcement learning, evolutionary algorithms and sequential model-based optimization have been used to learn network structures. <br />
<br />
3) Some other works focus on increasing model size, sharing model weights to accelerate model search or a continuous relaxation of the architecture representation. <br />
<br />
4) Some recent methods focus on proposing methods for embedding an exponentially large number of architectures in a grid arrangement for semantic segmentation tasks. <br />
<br />
In the area of multi-scale representation for dense image prediction the following are useful prior work: <br />
<br />
1) State of the art methods use Convolutional Neural Nets. There are different methods proposed for supplying global features and context information to perform pixel level classification. <br />
<br />
2) Some approaches focus on how to efficiently encode multi-scale context information in a network architecture like designing models that take an input an image pyramid so that large-scale objects are captured by the downsampled image. <br />
<br />
3) Research also tried to come up with a theme on how best to tune the architecture to extract context information. Some works focus on sampling rates in atrous convolution to encode multi-scale context. Some others build context module by gradually increasing the rate on top of belief maps.<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol><br />
The search space is easy to understand, for instance defining a hyperparameter space to consider for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumptions we make on the neural architecture. The search strategy details how to explore the search space. The evaluation strategy refers to taking an input of a set of hyperparameters, and from there evaluating how well our model fits. In the field of NAS, it is typical to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
The purpose of architecture search space is to design a space that can express various state-of-the-art architectures, and able to identify good models.<br />
<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|150px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|400px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|600px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC" which represented by a directed acyclic graph (DAG) with five branches (i.e. the optimal value, which gives a good balance between flexibility and computational tractability). A DAG is a finite directed graph with no directed cycles which consists of finitely many vertices and edges, with each edge directed from one vertex to another, such that there is no way to start at any vertex <math>v</math> and follow a consistently-directed sequence of edges that eventually loops back to <math>v</math> again. The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell, that is a recursive search space to encode multi-scale context information for dense prediction tasks. In theory, the search space consists of what they choose for the network backbone and the internal structure of the DPC. In practice, they just used MobileNet and Modified Xception net as the backbone. So the search space only consists of the internal structure of the DPC cell.<br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
For the spatial pyramid pooling operation, average pooling is performed in each grid. After the<br />
average pooling, a 1×1 convolution is applied and the then the resize back the features to have the same spatial resolution as the input tensor.<br />
<br />
Separable convolution with 256 filters is employed for all convolutions and 3x3 atrous convolutions with sampling rates rh x rw allows for capturing object scales with different aspect ratios. This is illustrated in the diagram below: <br />
<br />
[[File:NAS_fig2.png|center|500px]]<br />
<br />
Average spatial pyramid pooling is performs mean pooling on the last convolution layer (either convolution or sub sampling) and produces a N*B dimensional vector (where N=Number of filters in the convolution layer, B= Number of Bins). The vector is in turn fed to the fully connected layer. The number of bins is a constant value. Therefore, the vector dimension remains constant irrespective of the input image size.<br />
<br />
The resulting search space is able to encode all the main state-of-the-art architectures(i.e. Deformable Convnets [11], ASPP, Dense-ASPP [12] etc.), but these encoded architectures are more diverse since each branch of a DPC cell could build contextual information through parallel or cascaded representations. The number of potential architectures may determine the potential diversity of the search space. For <math display="inline">i</math>-th branch, there are <math display="inline">i</math> possible inputs, including the last feature maps produced by the network backbone, all the outputs from previous branch (<math display="inline">i.e., Y_1,...,Y_{i-1}</math>), and also 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in <math display="inline">i × 81</math> possible options. Therefore, for B = 5, the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|600px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
The pseudocode for a general random search algorithm is provided below.<br />
<br />
[[File:Pseudoc.png |700px|center]]<br />
<br />
It essentially repeatedly searches randomly within the hypersphere of the current state, and updates only if the reward function is increased when using the newly found vector. The approach is highly non-parametric, and is easily generalized for complex problems such as architectural finding once parameters are properly defined. Although Random Search can return a reasonable approximation of the optimal solution under low problem dimensionality, the approach is commonly cited to perform poorly under higher problem dimensionality. The implementation of Random Search within this context is used to find highly complex architectures with millions of parameters; this could explain the only marginal improvements to human created state-of-the art networks despite the heavy machinery used to arrive at new architectures in the experiments section.<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 800px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|1000px]]<br />
</div><br />
<br />
Table 2 describes the results on scene parsing dataset. It sets a new state-of-the-art performance of 82.7% mIOU and outperforms other state-of-the-art models across 11 of the 19 categories.<br />
<br />
Table 3 describes the results on person part segmentation dataset. It achieve the state-of-the-art performance of 71.34% mIOU and outperforms other state-of-the-art models across 6 of the 7 categories.<br />
<br />
Table 4 describes the results on semantic image segmentation dataset. It achieve the state-of-the-art performance of 87.9% mIOU and outperforms other state-of-the-art models across 6 of the 20 categories.<br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy. They hope that by using some meta learning on metadata it can lead to future insight and be advantageous. <br />
<br />
The author hope that this architecture search techniques can be ported into other domains such as depth prediction and object detection to achieve similar gains over human-invented designs.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
11. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei. Deformable convolutional networks. In ICCV, 2017.<br />
<br />
12. M. Yang, K. Yu, C. Zhang, Z. Li, and K. Yang. Denseaspp for semantic segmentation in street scenes. In CVPR, 2018.<br />
<br />
13. Elsken, Thomas, Jan Hendrik Metzen, and Frank Hutter. "Neural architecture search: A survey." arXiv preprint arXiv:1808.05377 (2018).</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=42242Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-12-03T07:05:19Z<p>A22ravi: /* What they used in this paper */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search (NAS) has emerged, which is to automatically find an optimal neural architecture for a given task in a well-defined architecture space. The resulting architectures have often outperform networks designed by human experts on tasks such as image classification and natural language processing. [2,3,4] <br />
<br />
This paper presents a meta-learning technique to have computers search for a neural architecture that performs well on the task of dense image segmentation, mainly focused on the problem of scene labeling.<br />
<br />
=Motivation=<br />
<br />
The part of deep neural networks(DNN) success is largely due to the fact that it greatly reduces the work in feature engineering. This is because DNNs have the ability to extract useful features given the raw input. However, this creates a new paradigm to look at - network engineering. In order to extract significant features, an appropriate network architecture must be used. Hence, the engineering work is shifted from feature engineering to network architecture design for better abstraction of features.<br />
<br />
The motivation for NAS is to establish a guiding theory behind how to design the optimal network architecture. Given that there is an <br />
abundant amount of computational resources available, an intuitive solution is to define a finite search space for a computer to search for optimal network structures and hyperparameters.<br />
<br />
=Related Work =<br />
<br />
This paper focuses on two main literature research topics. One is the neural architecture search (NAS) and the other is the Multi-Scale representation for dense image prediction. Neural architecture search trains a controller network to generate neural architectures. The following are the important research directions in this area: <br />
<br />
1) One kind of research transfers architectures learned on a proxy dataset to more challenging datasets and demonstrates superior performance over many human-invented architectures.<br />
<br />
2) Reinforcement learning, evolutionary algorithms and sequential model-based optimization have been used to learn network structures. <br />
<br />
3) Some other works focus on increasing model size, sharing model weights to accelerate model search or a continuous relaxation of the architecture representation. <br />
<br />
4) Some recent methods focus on proposing methods for embedding an exponentially large number of architectures in a grid arrangement for semantic segmentation tasks. <br />
<br />
In the area of multi-scale representation for dense image prediction the following are useful prior work: <br />
<br />
1) State of the art methods use Convolutional Neural Nets. There are different methods proposed for supplying global features and context information to perform pixel level classification. <br />
<br />
2) Some approaches focus on how to efficiently encode multi-scale context information in a network architecture like designing models that take an input an image pyramid so that large-scale objects are captured by the downsampled image. <br />
<br />
3) Research also tried to come up with a theme on how best to tune the architecture to extract context information. Some works focus on sampling rates in atrous convolution to encode multi-scale context. Some others build context module by gradually increasing the rate on top of belief maps.<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol><br />
The search space is easy to understand, for instance defining a hyperparameter space to consider for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumptions we make on the neural architecture. The search strategy details how to explore the search space. The evaluation strategy refers to taking an input of a set of hyperparameters, and from there evaluating how well our model fits. In the field of NAS, it is typical to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
The purpose of architecture search space is to design a space that can express various state-of-the-art architectures, and able to identify good models.<br />
<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|150px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|400px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|600px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC" which represented by a directed acyclic graph (DAG) with five branches (i.e. the optimal value, which gives a good balance between flexibility and computational tractability). A DAG is a finite directed graph with no directed cycles which consists of finitely many vertices and edges, with each edge directed from one vertex to another, such that there is no way to start at any vertex <math>v</math> and follow a consistently-directed sequence of edges that eventually loops back to <math>v</math> again. The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell, that is a recursive search space to encode multi-scale context information for dense prediction tasks. In theory, the search space consists of what they choose for the network backbone and the internal structure of the DPC. In practice, they just used MobileNet and Modified Xception net as the backbone. So the search space only consists of the internal structure of the DPC cell.<br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
For the spatial pyramid pooling operation, average pooling is performed in each grid. After the<br />
average pooling, a 1×1 convolution is applied and the then the resize back the features to have the same spatial resolution as the input tensor.<br />
<br />
Separable convolution with 256 filters is employed for all convolutions and 3x3 atrous convolutions with sampling rates rh x rw allows for capturing object scales with different aspect ratios. This is illustrated in the diagram below: <br />
<br />
[[File:NAS_fig2.png|center|500px]]<br />
<br />
Average spatial pyramid pooling is performs mean pooling on the last convolution layer (either convolution or sub sampling) and produces a N*B dimensional vector (where N=Number of filters in the convolution layer, B= Number of Bins). The vector is in turn fed to the fully connected layer. The number of bins is a constant value. Therefore, the vector dimension remains constant irrespective of the input image size.<br />
<br />
The resulting search space is able to encode all the main state-of-the-art architectures(i.e. Deformable Convnets [11], ASPP, Dense-ASPP [12] etc.), but these encoded architectures are more diverse since each branch of a DPC cell could build contextual information through parallel or cascaded representations. The number of potential architectures may determine the potential diversity of the search space. For <math display="inline">i</math>-th branch, there are <math display="inline">i</math> possible inputs, including the last feature maps produced by the network backbone, all the outputs from previous branch (<math display="inline">i.e., Y_1,...,Y_{i-1}</math>), and also 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in <math display="inline">i × 81</math> possible options. Therefore, for B = 5, the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|600px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
The pseudocode for a general random search algorithm is provided below.<br />
<br />
[[File:Pseudoc.png |700px|center]]<br />
<br />
It essentially repeatedly searches randomly within the hypersphere of the current state, and updates only if the reward function is increased when using the newly found vector. The approach is highly non-parametric, and is easily generalized for complex problems such as architectural finding once parameters are properly defined. Although Random Search can return a reasonable approximation of the optimal solution under low problem dimensionality, the approach is commonly cited to perform poorly under higher problem dimensionality. The implementation of Random Search within this context is used to find highly complex architectures with millions of parameters; this could explain the only marginal improvements to human created state-of-the art networks despite the heavy machinery used to arrive at new architectures in the experiments section.<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 800px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|1000px]]<br />
</div><br />
<br />
Table 2 describes the results on scene parsing dataset. It sets a new state-of-the-art performance of 82.7% mIOU and outperforms other state-of-the-art models across 11 of the 19 categories.<br />
<br />
Table 3 describes the results on person part segmentation dataset. It achieve the state-of-the-art performance of 71.34% mIOU and outperforms other state-of-the-art models across 6 of the 7 categories.<br />
<br />
Table 4 describes the results on semantic image segmentation dataset. It achieve the state-of-the-art performance of 87.9% mIOU and outperforms other state-of-the-art models across 6 of the 20 categories.<br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy. They hope that by using some meta learning on metadata it can lead to future insight and be advantageous. <br />
<br />
The author hope that this architecture search techniques can be ported into other domains such as depth prediction and object detection to achieve similar gains over human-invented designs.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
11. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei. Deformable convolutional networks. In ICCV, 2017.<br />
<br />
12. M. Yang, K. Yu, C. Zhang, Z. Li, and K. Yang. Denseaspp for semantic segmentation in street scenes. In CVPR, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=42241Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-12-03T07:05:04Z<p>A22ravi: /* What they used in this paper */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search (NAS) has emerged, which is to automatically find an optimal neural architecture for a given task in a well-defined architecture space. The resulting architectures have often outperform networks designed by human experts on tasks such as image classification and natural language processing. [2,3,4] <br />
<br />
This paper presents a meta-learning technique to have computers search for a neural architecture that performs well on the task of dense image segmentation, mainly focused on the problem of scene labeling.<br />
<br />
=Motivation=<br />
<br />
The part of deep neural networks(DNN) success is largely due to the fact that it greatly reduces the work in feature engineering. This is because DNNs have the ability to extract useful features given the raw input. However, this creates a new paradigm to look at - network engineering. In order to extract significant features, an appropriate network architecture must be used. Hence, the engineering work is shifted from feature engineering to network architecture design for better abstraction of features.<br />
<br />
The motivation for NAS is to establish a guiding theory behind how to design the optimal network architecture. Given that there is an <br />
abundant amount of computational resources available, an intuitive solution is to define a finite search space for a computer to search for optimal network structures and hyperparameters.<br />
<br />
=Related Work =<br />
<br />
This paper focuses on two main literature research topics. One is the neural architecture search (NAS) and the other is the Multi-Scale representation for dense image prediction. Neural architecture search trains a controller network to generate neural architectures. The following are the important research directions in this area: <br />
<br />
1) One kind of research transfers architectures learned on a proxy dataset to more challenging datasets and demonstrates superior performance over many human-invented architectures.<br />
<br />
2) Reinforcement learning, evolutionary algorithms and sequential model-based optimization have been used to learn network structures. <br />
<br />
3) Some other works focus on increasing model size, sharing model weights to accelerate model search or a continuous relaxation of the architecture representation. <br />
<br />
4) Some recent methods focus on proposing methods for embedding an exponentially large number of architectures in a grid arrangement for semantic segmentation tasks. <br />
<br />
In the area of multi-scale representation for dense image prediction the following are useful prior work: <br />
<br />
1) State of the art methods use Convolutional Neural Nets. There are different methods proposed for supplying global features and context information to perform pixel level classification. <br />
<br />
2) Some approaches focus on how to efficiently encode multi-scale context information in a network architecture like designing models that take an input an image pyramid so that large-scale objects are captured by the downsampled image. <br />
<br />
3) Research also tried to come up with a theme on how best to tune the architecture to extract context information. Some works focus on sampling rates in atrous convolution to encode multi-scale context. Some others build context module by gradually increasing the rate on top of belief maps.<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol><br />
The search space is easy to understand, for instance defining a hyperparameter space to consider for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumptions we make on the neural architecture. The search strategy details how to explore the search space. The evaluation strategy refers to taking an input of a set of hyperparameters, and from there evaluating how well our model fits. In the field of NAS, it is typical to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
The purpose of architecture search space is to design a space that can express various state-of-the-art architectures, and able to identify good models.<br />
<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|150px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|400px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|600px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC" which represented by a directed acyclic graph (DAG) with five branches (i.e. the optimal value, which gives a good balance between flexibility and computational tractability). A DAG is a finite directed graph with no directed cycles which consists of finitely many vertices and edges, with each edge directed from one vertex to another, such that there is no way to start at any vertex <math>v</math> and follow a consistently-directed sequence of edges that eventually loops back to <math>v</math> again. The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell, that is a recursive search space to encode multi-scale context information for dense prediction tasks. In theory, the search space consists of what they choose for the network backbone and the internal structure of the DPC. In practice, they just used MobileNet and Modified Xception net as the backbone. So the search space only consists of the internal structure of the DPC cell.<br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
For the spatial pyramid pooling operation, average pooling is performed in each grid. After the<br />
average pooling, a 1×1 convolution is applied and the then the resize back the features to have the same spatial resolution as the input tensor.<br />
<br />
Separable convolution with 256 filters is employed for all convolutions and 3x3 atrous convolutions with sampling rates rh x rw allows for capturing object scales with different aspect ratios. This is illustrated in the diagram below: <br />
<br />
[[File:NAS_fig2.png|center|500px]]<br />
<br />
<br />
Average spatial pyramid pooling is performs mean pooling on the last convolution layer (either convolution or sub sampling) and produces a N*B dimensional vector (where N=Number of filters in the convolution layer, B= Number of Bins). The vector is in turn fed to the fully connected layer. The number of bins is a constant value. Therefore, the vector dimension remains constant irrespective of the input image size.<br />
<br />
The resulting search space is able to encode all the main state-of-the-art architectures(i.e. Deformable Convnets [11], ASPP, Dense-ASPP [12] etc.), but these encoded architectures are more diverse since each branch of a DPC cell could build contextual information through parallel or cascaded representations. The number of potential architectures may determine the potential diversity of the search space. For <math display="inline">i</math>-th branch, there are <math display="inline">i</math> possible inputs, including the last feature maps produced by the network backbone, all the outputs from previous branch (<math display="inline">i.e., Y_1,...,Y_{i-1}</math>), and also 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in <math display="inline">i × 81</math> possible options. Therefore, for B = 5, the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|600px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
The pseudocode for a general random search algorithm is provided below.<br />
<br />
[[File:Pseudoc.png |700px|center]]<br />
<br />
It essentially repeatedly searches randomly within the hypersphere of the current state, and updates only if the reward function is increased when using the newly found vector. The approach is highly non-parametric, and is easily generalized for complex problems such as architectural finding once parameters are properly defined. Although Random Search can return a reasonable approximation of the optimal solution under low problem dimensionality, the approach is commonly cited to perform poorly under higher problem dimensionality. The implementation of Random Search within this context is used to find highly complex architectures with millions of parameters; this could explain the only marginal improvements to human created state-of-the art networks despite the heavy machinery used to arrive at new architectures in the experiments section.<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 800px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|1000px]]<br />
</div><br />
<br />
Table 2 describes the results on scene parsing dataset. It sets a new state-of-the-art performance of 82.7% mIOU and outperforms other state-of-the-art models across 11 of the 19 categories.<br />
<br />
Table 3 describes the results on person part segmentation dataset. It achieve the state-of-the-art performance of 71.34% mIOU and outperforms other state-of-the-art models across 6 of the 7 categories.<br />
<br />
Table 4 describes the results on semantic image segmentation dataset. It achieve the state-of-the-art performance of 87.9% mIOU and outperforms other state-of-the-art models across 6 of the 20 categories.<br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy. They hope that by using some meta learning on metadata it can lead to future insight and be advantageous. <br />
<br />
The author hope that this architecture search techniques can be ported into other domains such as depth prediction and object detection to achieve similar gains over human-invented designs.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
11. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei. Deformable convolutional networks. In ICCV, 2017.<br />
<br />
12. M. Yang, K. Yu, C. Zhang, Z. Li, and K. Yang. Denseaspp for semantic segmentation in street scenes. In CVPR, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:NAS_fig2.png&diff=42240File:NAS fig2.png2018-12-03T06:53:45Z<p>A22ravi: </p>
<hr />
<div></div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Co-Teaching&diff=42239Co-Teaching2018-12-03T06:39:46Z<p>A22ravi: /* Future Work */</p>
<hr />
<div>=Introduction=<br />
==Title of Paper==<br />
Co-teaching: Robust Training Deep Neural Networks with Extremely Noisy Labels<br />
==Contributions==<br />
The paper proposes a novel approach to training deep neural networks on data with noisy labels. The proposed architecture, named ‘co-teaching’, maintains two networks simultaneously, which focuses on training on selected clean instances and avoids estimating the noise transition matrix. In addition, using stochastic optimization with momentum to train the deep networks and clean data can be memorized by nonlinear deep networks, which becomes robust. The experiments are conducted on noisy versions of MNIST, CIFAR-10 and CIFAR-100 datasets. Empirical results demonstrate that, under extremely noisy circumstances (i.e., 45% of noisy labels), the robustness of deep learning models trained by the co-teaching approach is much superior to state-of-the-art baselines<br />
<br />
==Terminology==<br />
Ground-Truth Labels: The proper objective labels (i.e. the real, or ‘true’, labels) of the data. <br />
<br />
Noisy Labels: Labels that are corrupted (either manually or through the data collection process) from ground-truth labels. This can result in false positives.<br />
<br />
=Intuition=<br />
The Co-teaching architecture maintains two networks with different learning abilities simultaneously. The reason why Co-teaching is more robust can be explained as follows. Usually when learning on a batch of noisy data, only the error from the network itself is transferred back to facilitate learning. But in the case of Co-teaching, the two networks are able to filter different type of errors, and flow back to itself and the other network. As a result, the two models learn together, from the network itself and the partner network.<br />
<br />
=Motivation=<br />
The paper draws motivation from two key facts:<br />
• That many data collection processes yield noisy labels. <br />
• That deep neural networks have a high capacity to overfit to noisy labels. <br />
Because of these facts, it is challenging to train deep networks to be robust with noisy labels. <br />
=Related Works=<br />
<br />
1. Statistical learning methods: Some approaches use statistical learning methods for the problem of learning from extremely noisy labels. These approaches can be divided into 3 strands: surrogate loss, noise estimation, and probabilistic modelling. In the surrogate loss category, one work proposes an unbiased estimator to provide the noise corrected loss approach. Another work presented a robust non-convex loss, which is the special case in a family of robust losses. In the noise rate estimation category, some authors propose a class-probability estimator using order statistics on the range of scores. Another work presented the same estimator using the slope of ROC curve. In the probabilistic modelling category, there is a two coin model proposed to handle noise labels from multiple annotators. <br />
<br />
2. Deep learning methods: There are also deep learning approaches that can be used to approach data with noisy labels. One work proposed a unified framework to distill knowledge from clean labels and knowledge graphs. Another work trained a label cleaning network by a small set of clean labels and used it to reduce the noise in large-scale noisy labels. There is also a proposed joint optimization framework to learn parameters and estimate true labels simultaneously. <br />
Another work leverages an additional validation set to adaptively assign weights to training examples in every iteration. One particular paper ads a crowd layer after the output layer for noisy labels from multiple annotators. <br />
<br />
3. Learning to teach methods: It is another approach to this problem. The methods are made up by the teacher and student networks. The teacher network selects more informative instances for better training of student networks. Most works did not account for noisy labels, with exception to MentorNet, which applied the idea on data with noisy labels.<br />
<br />
=Co-Teaching Algorithm=<br />
<br />
[[File:Co-Teaching_Algorithm.png|600px|center]]<br />
<br />
The idea as shown in the algorithm above is to train two deep networks simultaneously. In each mini-batch using mini-batch gradient descent, each network selects its small-loss instances as useful knowledge and then teaches these useful instances to the peer network. <math>R(T)</math> governs the percentage of small-loss instances to be used in updating the parameters of each network.<br />
<br />
=Summary of Experiment=<br />
==Proposed Method==<br />
The proposed co-teaching method maintains two networks simultaneously, and samples instances with small loss at each mini batch. The sample of small-loss instances is then taught to the peer network. <br />
[[File:Co-Teaching Fig 1.png|600px|center]] <br />
The co-teaching method relies on research that suggests deep networks learn clean and easy patterns in initial epochs, but are susceptible to overfitting noisy labels as the number of epochs grows. To counteract this, the co-teaching method reduces the mini-batch size by gradually increasing a drop rate (i.e., noisy instances with higher loss will be dropped at an increasing rate). <br />
The mini-batches are swapped between peer networks due to the underlying intuition that different classifiers will generate different decision boundaries. Swapping the mini-batches constitutes a sort of ‘peer-reviewing’ that promotes noise reduction since the error from a network is not directly transferred back to itself. <br />
==Dataset Corruption==<br />
The datasets incorporated by this paper include MNIST, CIFAR-10 and CIFAR-100. A summary of these datasets are shown as below. <br />
<br />
[[File:co_teaching_data.png|600px|center]] <br />
<br />
To simulate learning with noisy labels, the datasets (which are clean by default) are manually corrupted by applying a noise transformation matrix<math>Q</math>, where where <math>Q_{ij} = Pr(\widetilde{y} = j|y = i)</math> given that noisy <math>\widetilde{y}</math> is flipped from clean <math>y</math>. Two methods are used for generating such noise transformation matrices: pair flipping and symmetry. <br />
[[File:Co-Teaching Fig 2.png|600px|center]] <br />
Three noise conditions are simulated for comparing co-teaching with baseline methods.<br />
<br />
Note: Corruption of Dataset here means randomly choosing a wrong label instead of the target label by applying noise. <br />
<br />
{| class="wikitable"<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Method<br />
|width="100pt"|Noise Rate<br />
|width="700pt"|Rationale<br />
|-<br />
| Pair Flipping || 45% || Almost half of the instances have noisy labels. Simulates erroneous labels which are similar to true labels. <br />
|-<br />
| Symmetry || 50% || Half of the instances have noisy labels. Labels have a constant probability of being corrupted. Further rationale can be found at [1].<br />
|-<br />
| Symmetry || 20% || Verify the robustness of co-teaching in a low-level noise scenario. <br />
|}<br />
|}<br />
<br />
==Baseline Comparisons==<br />
The co-teaching method is compared with several baseline approaches, which have varying:<br />
• proficiency in dealing with a large number of classes,<br />
• ability to resist heavy noise,<br />
• need to combine with specific network architectures, and<br />
• need to be pretrained. <br />
<br />
[[File:Co-Teaching Fig 3.png|600px|center]] <br />
===Bootstrap===<br />
The general idea behind bootstrapping is to dynamically change (correct) noisy labels during training. The idea is to take a value derived from the original and predicted class. The final label is some convex combination of the two. It should be noted that the weighting of the prediction is increased over time to account for the model itself improving. Of course, this procedure needs to be finely tuned to prevent it from rampantly changing correct labels before it becomes accurate. [2].<br />
<br />
===S-Model===<br />
Using an additional softmax layer to model the noise transition matrix [3].<br />
===F-Correction===<br />
Correcting the prediction by using a noise transition matrix which is estimated by a standard network [4].<br />
===Decoupling===<br />
Two separate classifiers are used in this technique. Parameters are updated using only the samples that are classified differently between the two models [5].<br />
===MentorNet===<br />
A mentor network is weights the probability of data instances being clean/noisy in order to train the student network on cleaner instances [6].<br />
<br />
As shown in the above table - few of the advantages of Co-teaaching method include - Co-teaching<br />
method does not rely on any specific network architectures, which can also deal with a large number of classes and is more robust to noise. Besides, it can be trained from scratch.This makes teaching more appealing for practical usage.<br />
<br />
==Implementation Details==<br />
Two CNN models using the same architecture (shown below) are used as the peer networks for the co-teaching method. They are initialized with different parameters in order to be significantly different from one another (different initial parameters can lead to different local minima). An Adam optimizer (momentum=0.9), a learning rate of 0.001, a batch size of 128, and 200 epochs are used for each dataset. The networks also utilize dropout and batch normalization. <br />
<br />
[[File: Co-Teaching Table 3.png|center]] <br />
=Results and Discussion=<br />
The co-teaching algorithm is compared to the baseline approaches under the noise conditions previously described. The results are as follows. <br />
==MNIST==<br />
The results of testing on the MNIST dataset are shown below. The Symmetry-20% case can be taken as a near-baseline; all methods perform well. However, under the Symmetry-50% case, all methods except MentorNet and Co-Teaching drop below 90% accuracy. Under the Pair-45% case, all methods except MentorNet and Co-Teaching drop below 60%. Under both high-noise conditions, the Co-Teaching method produces the highest accuracy. Similar patterns can be seen in the two additional sets of test results, though the specific accuracy values are different. Co-Teaching performs best under the high-noise situations<br />
<br />
The images labelled 'Figure 3' show test accuracy with respect to epoch of the various algorithms. Many algorithms show evidence of over-fitting or being influenced by noisy data, after reaching initial high accuracy. MentorNet and Co-Teaching experience this less than other methods, and Co-Teaching generally achieves higher accuracy than MentorNet. <br />
<br />
Robustness of the proposed method to noise which plays an important rule in the evaluation, is evident in the plots which is better or comparable to the other methods.<br />
<br />
[[File:Co-Teaching Table 4.png|550px|center]]<br />
<br />
[[File:Co-Teaching Graphs MNIST.PNG|center]]<br />
<br />
==CIFAR10==<br />
The observations here are consistently the same as these for MNIST dataset.<br />
[[File:Co-Teaching Table 5.png|550px|center]] <br />
<br />
[[File:Co-Teaching Graphs CIFAR10.PNG|center]]<br />
==CIFAR100==<br />
[[File:Co-Teaching Table 6.png|550px|center]] <br />
<br />
[[File: Co-Teaching Graphs CIFAR100.PNG|center]]<br />
==Choice of R(T) and <math> \tau</math>==<br />
There were some principles they followed when it came to choosing R(T) and <math> \tau</math>. R(T)=1, there was no instance needed at the beginning. They could safely update parameters in the early stage using the whole noise data since the deep neural networks would not memorize the noisy data. However, they need to drop more instances at the later stage. Because the model would eventually try to fit noisy data.<br />
<br />
R(T)=1-<math> \tau </math> *min{<math>T^{c}/T_{k},1 </math>} with <math> \tau=\epsilon </math>, where <math> \epsilon </math> is noise level.<br />
In this case, we consider c={0.5,1,2}. From Table 7, the test accuracy is stable.<br />
<br />
[[File: Co-Teaching Table 7.png|550px|center]] <br />
<br />
For <math> \tau</math>, we consider <math> \tau={0.5,0.75,1,1.25,1.5}\epsilon</math>. From Table 8, the performance can be improved with dropping more instances.<br />
[[File: Co-Teaching Table 8.png|550px|center]]<br />
<br />
=Conclusions=<br />
The main goal of the paper is to introduce the “Co-teaching” learning paradigm that uses two deep neural networks learning simultaneously to avoid noisy labels. Experiments are performed on several datasets such as MNIST, CIFAR-10, and CIFAR-100. The performance varied depending on the noise level in different scenarios. In the simulated ‘extreme noise’ scenarios, (pair-45% and symmetry-50%), the co-teaching methods outperforms baseline methods in terms of accuracy. This suggests that the co-teaching method is superior to the baseline methods in scenarios of extreme noise. The co-teaching method also performs competitively in the low-noise scenario (symmetry-20%).<br />
<br />
=Future Work=<br />
For future work, the paper can be extended in following ways: First , the the Co-teaching program can be adapted to train deep models under weak supervisions , e.g positive and unlabeled data. Second theoretical guarantees for Co-teaching can be investigated. The current approach seems to be have potential application in eliminating noisy labels/data from biomedical signals for example in the case of EEG data. This is important as EEG data are generally collected based on an experimental protocol and under controlled lab conditions. When data is collected in this way, even though the underlying brain process does not correspond to the EEG signals being collected, they can be labelled incorrectly based on the experimental protocol. Such cases of wrong labeling/data need to be eliminated from the training process and this is one scenario where co-teaching could possibly be applied. Also, this method seems to have potential application in data collected via crowd-sourcing or same data being labelled by multiple human subjects. Further, there is no analysis for generalization performance on deep learning with noisy labels which can also be studied in future.<br />
<br />
=Critique=<br />
The paper evaluates the performance considering the complexity of computations and implementations of the algorithms. Co-teaching methodology seems an interesting idea but can possibly become tricky to implement. Technically, such complexity can negatively impact the performance of the algorithm. <br />
==Lack of Task Diversity==<br />
The datasets used in this experiment are all image classification tasks – these results may not generalize to other deep learning applications, such as classifications from data with lower or higher dimensionality. <br />
==Needs to be expanded to other weak supervisions (Mentioned in conclusion)==<br />
Adaptation of the co-teaching method to train under other weak supervision (e.g. positive and unlabeled data) could expand the applicability of the paradigm. <br />
==Lack of Theoretical Development (Mentioned in conclusion)==<br />
This paper lacks any theoretical guarantees for co-teaching. Proving that the results shown in this study are generalizable would bolster the findings significantly.<br />
<br />
=References=<br />
[1] B. Van Rooyen, A. Menon, and B. Williamson. Learning with symmetric label noise: The<br />
importance of being unhinged. In NIPS, 2015.<br />
<br />
[2] S. Reed, H. Lee, D. Anguelov, C. Szegedy, D. Erhan, and A. Rabinovich. Training deep neural<br />
networks on noisy labels with bootstrapping. In ICLR, 2015.<br />
<br />
[3] J. Goldberger and E. Ben-Reuven. Training deep neural-networks using a noise adaptation layer.<br />
In ICLR, 2017.<br />
<br />
[4] G. Patrini, A. Rozza, A. Menon, R. Nock, and L. Qu. Making deep neural networks robust to<br />
label noise: A loss correction approach. In CVPR, 2017.<br />
<br />
[5] E. Malach and S. Shalev-Shwartz. Decoupling" when to update" from" how to update". In<br />
NIPS, 2017.<br />
<br />
[6] L. Jiang, Z. Zhou, T. Leung, L. Li, and L. Fei-Fei. Mentornet: Learning data-driven curriculum<br />
for very deep neural networks on corrupted labels. In ICML, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Co-Teaching&diff=42238Co-Teaching2018-12-03T06:32:24Z<p>A22ravi: /* Critique */</p>
<hr />
<div>=Introduction=<br />
==Title of Paper==<br />
Co-teaching: Robust Training Deep Neural Networks with Extremely Noisy Labels<br />
==Contributions==<br />
The paper proposes a novel approach to training deep neural networks on data with noisy labels. The proposed architecture, named ‘co-teaching’, maintains two networks simultaneously, which focuses on training on selected clean instances and avoids estimating the noise transition matrix. In addition, using stochastic optimization with momentum to train the deep networks and clean data can be memorized by nonlinear deep networks, which becomes robust. The experiments are conducted on noisy versions of MNIST, CIFAR-10 and CIFAR-100 datasets. Empirical results demonstrate that, under extremely noisy circumstances (i.e., 45% of noisy labels), the robustness of deep learning models trained by the co-teaching approach is much superior to state-of-the-art baselines<br />
<br />
==Terminology==<br />
Ground-Truth Labels: The proper objective labels (i.e. the real, or ‘true’, labels) of the data. <br />
<br />
Noisy Labels: Labels that are corrupted (either manually or through the data collection process) from ground-truth labels. This can result in false positives.<br />
<br />
=Intuition=<br />
The Co-teaching architecture maintains two networks with different learning abilities simultaneously. The reason why Co-teaching is more robust can be explained as follows. Usually when learning on a batch of noisy data, only the error from the network itself is transferred back to facilitate learning. But in the case of Co-teaching, the two networks are able to filter different type of errors, and flow back to itself and the other network. As a result, the two models learn together, from the network itself and the partner network.<br />
<br />
=Motivation=<br />
The paper draws motivation from two key facts:<br />
• That many data collection processes yield noisy labels. <br />
• That deep neural networks have a high capacity to overfit to noisy labels. <br />
Because of these facts, it is challenging to train deep networks to be robust with noisy labels. <br />
=Related Works=<br />
<br />
1. Statistical learning methods: Some approaches use statistical learning methods for the problem of learning from extremely noisy labels. These approaches can be divided into 3 strands: surrogate loss, noise estimation, and probabilistic modelling. In the surrogate loss category, one work proposes an unbiased estimator to provide the noise corrected loss approach. Another work presented a robust non-convex loss, which is the special case in a family of robust losses. In the noise rate estimation category, some authors propose a class-probability estimator using order statistics on the range of scores. Another work presented the same estimator using the slope of ROC curve. In the probabilistic modelling category, there is a two coin model proposed to handle noise labels from multiple annotators. <br />
<br />
2. Deep learning methods: There are also deep learning approaches that can be used to approach data with noisy labels. One work proposed a unified framework to distill knowledge from clean labels and knowledge graphs. Another work trained a label cleaning network by a small set of clean labels and used it to reduce the noise in large-scale noisy labels. There is also a proposed joint optimization framework to learn parameters and estimate true labels simultaneously. <br />
Another work leverages an additional validation set to adaptively assign weights to training examples in every iteration. One particular paper ads a crowd layer after the output layer for noisy labels from multiple annotators. <br />
<br />
3. Learning to teach methods: It is another approach to this problem. The methods are made up by the teacher and student networks. The teacher network selects more informative instances for better training of student networks. Most works did not account for noisy labels, with exception to MentorNet, which applied the idea on data with noisy labels.<br />
<br />
=Co-Teaching Algorithm=<br />
<br />
[[File:Co-Teaching_Algorithm.png|600px|center]]<br />
<br />
The idea as shown in the algorithm above is to train two deep networks simultaneously. In each mini-batch using mini-batch gradient descent, each network selects its small-loss instances as useful knowledge and then teaches these useful instances to the peer network. <math>R(T)</math> governs the percentage of small-loss instances to be used in updating the parameters of each network.<br />
<br />
=Summary of Experiment=<br />
==Proposed Method==<br />
The proposed co-teaching method maintains two networks simultaneously, and samples instances with small loss at each mini batch. The sample of small-loss instances is then taught to the peer network. <br />
[[File:Co-Teaching Fig 1.png|600px|center]] <br />
The co-teaching method relies on research that suggests deep networks learn clean and easy patterns in initial epochs, but are susceptible to overfitting noisy labels as the number of epochs grows. To counteract this, the co-teaching method reduces the mini-batch size by gradually increasing a drop rate (i.e., noisy instances with higher loss will be dropped at an increasing rate). <br />
The mini-batches are swapped between peer networks due to the underlying intuition that different classifiers will generate different decision boundaries. Swapping the mini-batches constitutes a sort of ‘peer-reviewing’ that promotes noise reduction since the error from a network is not directly transferred back to itself. <br />
==Dataset Corruption==<br />
The datasets incorporated by this paper include MNIST, CIFAR-10 and CIFAR-100. A summary of these datasets are shown as below. <br />
<br />
[[File:co_teaching_data.png|600px|center]] <br />
<br />
To simulate learning with noisy labels, the datasets (which are clean by default) are manually corrupted by applying a noise transformation matrix<math>Q</math>, where where <math>Q_{ij} = Pr(\widetilde{y} = j|y = i)</math> given that noisy <math>\widetilde{y}</math> is flipped from clean <math>y</math>. Two methods are used for generating such noise transformation matrices: pair flipping and symmetry. <br />
[[File:Co-Teaching Fig 2.png|600px|center]] <br />
Three noise conditions are simulated for comparing co-teaching with baseline methods.<br />
<br />
Note: Corruption of Dataset here means randomly choosing a wrong label instead of the target label by applying noise. <br />
<br />
{| class="wikitable"<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Method<br />
|width="100pt"|Noise Rate<br />
|width="700pt"|Rationale<br />
|-<br />
| Pair Flipping || 45% || Almost half of the instances have noisy labels. Simulates erroneous labels which are similar to true labels. <br />
|-<br />
| Symmetry || 50% || Half of the instances have noisy labels. Labels have a constant probability of being corrupted. Further rationale can be found at [1].<br />
|-<br />
| Symmetry || 20% || Verify the robustness of co-teaching in a low-level noise scenario. <br />
|}<br />
|}<br />
<br />
==Baseline Comparisons==<br />
The co-teaching method is compared with several baseline approaches, which have varying:<br />
• proficiency in dealing with a large number of classes,<br />
• ability to resist heavy noise,<br />
• need to combine with specific network architectures, and<br />
• need to be pretrained. <br />
<br />
[[File:Co-Teaching Fig 3.png|600px|center]] <br />
===Bootstrap===<br />
The general idea behind bootstrapping is to dynamically change (correct) noisy labels during training. The idea is to take a value derived from the original and predicted class. The final label is some convex combination of the two. It should be noted that the weighting of the prediction is increased over time to account for the model itself improving. Of course, this procedure needs to be finely tuned to prevent it from rampantly changing correct labels before it becomes accurate. [2].<br />
<br />
===S-Model===<br />
Using an additional softmax layer to model the noise transition matrix [3].<br />
===F-Correction===<br />
Correcting the prediction by using a noise transition matrix which is estimated by a standard network [4].<br />
===Decoupling===<br />
Two separate classifiers are used in this technique. Parameters are updated using only the samples that are classified differently between the two models [5].<br />
===MentorNet===<br />
A mentor network is weights the probability of data instances being clean/noisy in order to train the student network on cleaner instances [6].<br />
<br />
As shown in the above table - few of the advantages of Co-teaaching method include - Co-teaching<br />
method does not rely on any specific network architectures, which can also deal with a large number of classes and is more robust to noise. Besides, it can be trained from scratch.This makes teaching more appealing for practical usage.<br />
<br />
==Implementation Details==<br />
Two CNN models using the same architecture (shown below) are used as the peer networks for the co-teaching method. They are initialized with different parameters in order to be significantly different from one another (different initial parameters can lead to different local minima). An Adam optimizer (momentum=0.9), a learning rate of 0.001, a batch size of 128, and 200 epochs are used for each dataset. The networks also utilize dropout and batch normalization. <br />
<br />
[[File: Co-Teaching Table 3.png|center]] <br />
=Results and Discussion=<br />
The co-teaching algorithm is compared to the baseline approaches under the noise conditions previously described. The results are as follows. <br />
==MNIST==<br />
The results of testing on the MNIST dataset are shown below. The Symmetry-20% case can be taken as a near-baseline; all methods perform well. However, under the Symmetry-50% case, all methods except MentorNet and Co-Teaching drop below 90% accuracy. Under the Pair-45% case, all methods except MentorNet and Co-Teaching drop below 60%. Under both high-noise conditions, the Co-Teaching method produces the highest accuracy. Similar patterns can be seen in the two additional sets of test results, though the specific accuracy values are different. Co-Teaching performs best under the high-noise situations<br />
<br />
The images labelled 'Figure 3' show test accuracy with respect to epoch of the various algorithms. Many algorithms show evidence of over-fitting or being influenced by noisy data, after reaching initial high accuracy. MentorNet and Co-Teaching experience this less than other methods, and Co-Teaching generally achieves higher accuracy than MentorNet. <br />
<br />
Robustness of the proposed method to noise which plays an important rule in the evaluation, is evident in the plots which is better or comparable to the other methods.<br />
<br />
[[File:Co-Teaching Table 4.png|550px|center]]<br />
<br />
[[File:Co-Teaching Graphs MNIST.PNG|center]]<br />
<br />
==CIFAR10==<br />
The observations here are consistently the same as these for MNIST dataset.<br />
[[File:Co-Teaching Table 5.png|550px|center]] <br />
<br />
[[File:Co-Teaching Graphs CIFAR10.PNG|center]]<br />
==CIFAR100==<br />
[[File:Co-Teaching Table 6.png|550px|center]] <br />
<br />
[[File: Co-Teaching Graphs CIFAR100.PNG|center]]<br />
==Choice of R(T) and <math> \tau</math>==<br />
There were some principles they followed when it came to choosing R(T) and <math> \tau</math>. R(T)=1, there was no instance needed at the beginning. They could safely update parameters in the early stage using the whole noise data since the deep neural networks would not memorize the noisy data. However, they need to drop more instances at the later stage. Because the model would eventually try to fit noisy data.<br />
<br />
R(T)=1-<math> \tau </math> *min{<math>T^{c}/T_{k},1 </math>} with <math> \tau=\epsilon </math>, where <math> \epsilon </math> is noise level.<br />
In this case, we consider c={0.5,1,2}. From Table 7, the test accuracy is stable.<br />
<br />
[[File: Co-Teaching Table 7.png|550px|center]] <br />
<br />
For <math> \tau</math>, we consider <math> \tau={0.5,0.75,1,1.25,1.5}\epsilon</math>. From Table 8, the performance can be improved with dropping more instances.<br />
[[File: Co-Teaching Table 8.png|550px|center]]<br />
<br />
=Conclusions=<br />
The main goal of the paper is to introduce the “Co-teaching” learning paradigm that uses two deep neural networks learning simultaneously to avoid noisy labels. Experiments are performed on several datasets such as MNIST, CIFAR-10, and CIFAR-100. The performance varied depending on the noise level in different scenarios. In the simulated ‘extreme noise’ scenarios, (pair-45% and symmetry-50%), the co-teaching methods outperforms baseline methods in terms of accuracy. This suggests that the co-teaching method is superior to the baseline methods in scenarios of extreme noise. The co-teaching method also performs competitively in the low-noise scenario (symmetry-20%).<br />
<br />
=Future Work=<br />
For future work, the paper can be extended in following ways: First , the the Co-teaching program can be adapted to train deep models under weak supervisions , e.g positive and unlabeled data. Second theoretical guarantees for Co-teaching can be investigated. Further , there is no analysis for generalization performance on deep learning with noisy labels which can also be studied in future.<br />
<br />
=Critique=<br />
The paper evaluates the performance considering the complexity of computations and implementations of the algorithms. Co-teaching methodology seems an interesting idea but can possibly become tricky to implement. Technically, such complexity can negatively impact the performance of the algorithm. <br />
==Lack of Task Diversity==<br />
The datasets used in this experiment are all image classification tasks – these results may not generalize to other deep learning applications, such as classifications from data with lower or higher dimensionality. <br />
==Needs to be expanded to other weak supervisions (Mentioned in conclusion)==<br />
Adaptation of the co-teaching method to train under other weak supervision (e.g. positive and unlabeled data) could expand the applicability of the paradigm. <br />
==Lack of Theoretical Development (Mentioned in conclusion)==<br />
This paper lacks any theoretical guarantees for co-teaching. Proving that the results shown in this study are generalizable would bolster the findings significantly.<br />
<br />
=References=<br />
[1] B. Van Rooyen, A. Menon, and B. Williamson. Learning with symmetric label noise: The<br />
importance of being unhinged. In NIPS, 2015.<br />
<br />
[2] S. Reed, H. Lee, D. Anguelov, C. Szegedy, D. Erhan, and A. Rabinovich. Training deep neural<br />
networks on noisy labels with bootstrapping. In ICLR, 2015.<br />
<br />
[3] J. Goldberger and E. Ben-Reuven. Training deep neural-networks using a noise adaptation layer.<br />
In ICLR, 2017.<br />
<br />
[4] G. Patrini, A. Rozza, A. Menon, R. Nock, and L. Qu. Making deep neural networks robust to<br />
label noise: A loss correction approach. In CVPR, 2017.<br />
<br />
[5] E. Malach and S. Shalev-Shwartz. Decoupling" when to update" from" how to update". In<br />
NIPS, 2017.<br />
<br />
[6] L. Jiang, Z. Zhou, T. Leung, L. Li, and L. Fei-Fei. Mentornet: Learning data-driven curriculum<br />
for very deep neural networks on corrupted labels. In ICML, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data&diff=42237Predicting Floor Level For 911 Calls with Neural Network and Smartphone Sensor Data2018-12-03T03:59:02Z<p>A22ravi: /* Critique */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
In highly populated cities with many buildings, locating individuals in the case of an emergency is an important task. For emergency responders, time is of essence. Therefore, accurately locating a 911 caller plays an integral role in this important process.<br />
<br />
The motivation for this problem is in the context of 911 calls: victims trapped in a tall building who seek immediate medical attention, locating emergency personnel such as firefighters or paramedics, or a minor calling on behalf of an incapacitated adult. <br />
<br />
In this paper, a novel approach is presented to accurately predict floor level for 911 calls by leveraging neural networks and sensor data from smartphones.<br />
<br />
In large cities with tall buildings, relying on GPS or Wi-Fi signals does not always lead to an accurate location of a caller.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:17floor.png|250px]]<br />
[[File:19floor.png|250px]]</div><br />
<br />
<br />
In this work, there are two major contributions. The first is that they trained a LSTM to classify whether a smartphone was either inside or outside a building using GPS, Received signal strength indication (RSSI), and magnetometer sensor readings. The model is compared with baseline models like feed-forward neural networks, logistic regression, SVM, HMM, and Random Forests. The second contribution is an algorithm, which uses the output of the trained LSTM, to predict change in the barometric pressure of the smartphone from when it first entered the building against that of its current location within the building. In the final part of their algorithm, they are able to predict the floor level by clustering the measurements of height.<br />
<br />
The model does not rely on the external sensors placed inside the building, prior knowledge of the building, nor user movement behaviour. The only input it looks at is the GPS and the barometric signal from the phone. Finally, they also talk about the application of this algorithm in a variety of other real-world situations. <br />
<br />
All the codes and data related to this article are available here[[https://github.com/williamFalcon/Predicting-floor-level-for-911-Calls-with-Neural-Networks-and-Smartphone-Sensor-Data]]<br />
<br />
=Related Work=<br />
<br />
<br />
In general, previous work falls under two categories. The first category of methods is the classification methods based on the user's activity. <br />
Therefore, some current methods leverage the user's activity to predict which is based on the offset in their movement [2]. These activities include running, walking, and moving through the elevator.<br />
The second set of methods focus more on the use of a barometer which measures the atmospheric pressure. As a result, utilizing a barometer can provide the changes in altitude.<br />
<br />
Avinash Parnandi and his coauthors used multiple classifiers in the predicting the floor level [2]. The steps in their algorithmic process are: <br />
<ol><br />
<li> Classifier to predict whether the user is indoors or outdoors</li><br />
<li> Classifier to identify if the activity of the user, i.e. walking, standing still etc. </li><br />
<li> Classifier to measure the displacement</li><br />
</ol><br />
<br />
One of the downsides of this work is to achieve the high accuracy that the user's step size is needed, therefore heavily relying on pre-training to the specific users. In a real world application of this method, this would not be practical.<br />
<br />
<br />
Song and his colleagues model the way or cause of ascent. That is, was the ascent a result of taking the elevator, stairs or escalator [3]. Then by using infrastructure support of the buildings and as well as additional tuning they are able to predict floor level. <br />
This method also suffers from relying on data specific to the building. <br />
<br />
Overall, these methods suffer from relying on pre-training to a specific user, needing additional infrastructure support, or data specific to the building. The method proposed in this paper aims to predict floor level without these constraints.<br />
<br />
=Method=<br />
<br />
<br />
In their paper, the authors claim that to their knowledge "there does not exist a dataset for predicting floor heights" [4].<br />
<br />
To collect data, the authors developed an iOS application (called Sensory) that runs on an iPhone 6s to aggregate the data. They used the smartphone's sensors to record different features such as barometric pressure, GPS course, GPS speed, RSSI strength, GPS longitude, GPS latitude, and altitude. The app streamed data at 1 sample per second, and each datum contained the different sensor measurements mentions earlier along with environment contexts like building floors, environment activity, city name, country name, and magnetic strength.<br />
<br />
The data collection procedure for '''indoor-outdoor classifier''' was described as follows:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) As soon as we exit, set indoors to 0. 7) Stop recording. 8) Save data as CSV for analysis. This procedure can start either outside or inside a building without loss of generality.<br />
<br />
The following procedure generates data used to '''predict a floor change''' from the entrance floor to the end floor:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) Finally, enter a building and ascend/descend to any story. 7) Ascend through any method desired, stairs, elevator, escalator, etc. 8) Once at the floor, stop recording. 9) Save data as CSV for analysis.<br />
<br />
Their algorithm was used to predict floor level which is a 3 part process:<br />
<br />
<ol><br />
<li> Classifying whether smartphone is indoor or outdoor </li><br />
<li> Indoor/Outdoor Transition detector</li><br />
<li> Estimating vertical height and resolving to absolute floor level </li><br />
</ol><br />
<br />
==1) Classifying Indoor/Outdoor ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:classifierfloor.png|800px]] </div><br />
<br />
From [5] they are using 6 features which were found through forests of trees feature reduction. The features are smartphone's barometric pressure (<math>P</math>), GPS vertical accuracy (<math>GV</math>), GPS horizontal accuracy (<math>GH</math>), GPS speed (<math>S</math>), device RSSI level (<math>rssi</math>), and magnetometer total reading (<math>M</math>).<br />
<br />
The magnetometer total reading was calculated from given the 3-dimensional reading <math>x, y, z </math><br />
<br />
<br />
<div style="text-align: center;">Total Magnetic field strength <math>= M = \sqrt{x^{2} + y^{2} + z^{2}}</math></div><br />
<br />
They used a 3 layer LSTM where the inputs are <math> d </math> consecutive time steps. The output <math> y = 1 </math> if smartphone is indoor and <math> y = 0 </math> if smartphone is outdoor.<br />
<br />
In their design they set <math> d = 3</math> by random search [6]. The point to make is that they wanted the network to learn the relationship given a little bit of information from both the past and future.<br />
<br />
For the overall signal sequence: <math> \{x_1, x_2,x_j, ... , x_n\}</math> the aim is to classify <math> d </math> consecutive sensor readings <math> X_i = \{x_1, x_2, ..., x_d \} </math> as <math> y = 1 </math> or <math> y = 0 </math> as noted above.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Table5.png|750px]] </div><br />
<br />
This is a critical part of their system and they only focus on the predictions in the subspace of being indoors. <br />
<br />
They have trained the LSTM to minimize the binary cross entropy between the true indoor state <math> y </math> of example <math> i </math>. <br />
<br />
The cost function is shown below:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:costfunction.png|450px]] </div><br />
<br />
The final output of the LSTM is a time-series <math> T = {t_1, t_2, ..., t_i, t_n} </math> where each <math> t_i = 0, t_i = 1 </math> if the point is outside or inside respectively.<br />
<br />
==2) Transition Detector ==<br />
<br />
Given the predictions from the previous step, now the next part is to find when the transition of going in or out of a building has occurred.<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:transition.png|400px]] </div><br />
In this figure, they convolve filters <math> V_1, V_2</math> across the predictions T and they pick a subset <math>s_i </math> such that the Jacard distance (defined below) is <math> >= 0.4 </math><br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:v1v2.png|250px]] </div><br />
Jacard Distance:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:jacard.png|450px]]</div><br />
<br />
After this process, we are now left with a set of <math> b_i</math>'s describing the index of each indoor/outdoor transition. The process is shown in the first figure.<br />
<br />
==3) Vertical height and floor level ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:resolvefloor.png|700px]] </div><br />
<br />
[3] suggested the use of a reference barometer or beacons as a way to determine the entrances to a building.<br />
<br />
However, such need is eliminated by the authors' approach. The authors' second key contribution is to use the LSTM IO predictions to help identifying these indoor transitions into the building. The LSTM provides a self-contained estimator of a building’s entrance without relying on external sensor information on a user’s body or beacons placed inside a building’s lobby. [4]<br />
<br />
In the final part of the system, the vertical offset needs to be computed given the smartphone's last known location i.e. the last known transition which can easily be computed given the set of transitions from the previous step. All that needs to be done is to pull the index of most recent transition from the previous step and set <math> p_0</math> to the lowest pressure within a ~ 15-second window around that index.<br />
<br />
The second parameter is <math> p_1 </math> which is the current pressure reading. In order to generate the relative change in height <math> m_\Delta</math><br />
<br />
After plugging this into the formula defined above we are now left with a scalar value which represents the height displacement between the entrance and the smartphone's current location of the building [7].<br />
<br />
In order to resolve to an absolute floor level, they use the index number of the clusters of <math> m_\Delta</math> 's. As seen above <math> 5.1 </math> is the third cluster implying floor number 3.<br />
<br />
=Experiments and Results=<br />
<br />
==Dataset==<br />
<br />
In this paper, an iOS app called Sensory is developed which is used to collect data on an iPhone 6. The following sensor readings were recorded: '''indoors''', '''created at''', '''session id''', '''floor''', '''RSSI strength''', '''GPS latitude''', '''GPS longitude''', '''GPS vertical accuracy''', '''GPS horizontal accuracy''', '''GPS course''', '''GPS speed''', '''barometric relative altitude''', '''barometric pressure''', '''environment context''', '''environment mean building floors''', '''environment activity''', '''city name''', '''country name''', '''magnet x''', '''magnet y''', '''magnet z''', '''magnet total'''.<br />
<br />
As soon as the user enters or exits a building, the indoor-outdoor data has to be manually entered. To gather the data for the floor level prediction, the authors conducted 63 trials among five different buildings throughout New York City. Since unsupervised learning was being used, the actual floor level was recorded manually for the validation purposes only.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:ioaccuracy.png|450px]] </div><br />
<br />
All of these classifiers were trained and validated on data from a total of 5082 data points. The set split was 80% training and 20% validation. <br />
For the LSTM the network was trained for a total of 24 epochs with a batch size of 128 and using an Adam optimizer where the learning rate was 0.006. <br />
Although the baselines performed considerably well the objective here was to show that an LSTM can be used in the future to model the entire system with an LSTM.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:flooraccuracy.png|650px]] </div><br />
<br />
The above chart shows the success that their system is able to achieve in the floor level prediction.<br />
<br />
The performance was measured in terms of how many floors were travelled rather than the absolute floor number. Because different buildings might have their floors differently numbered. They used different m values in 2 tests. One applies the same m value across all building and the other one applied specific m values on different buildings. The result showed that this specification on m values hugely increased the accuracy.<br />
<br />
=Future Work=<br />
The first part of the system used an LSTM for indoor/outdoor classification. Therefore, this separate module can be used in many other location problems. Working on this separate problem seems to be an approach that the authors will take. They also would like to aim towards modeling the whole problem within the LSTM in order to generate the floor level predictions solely from sensor reading data.<br />
<br />
=Critique=<br />
<br />
In this paper, the authors presented a novel system which can predict a smartphone's floor level with 100% accuracy, which has not been done. Previous work relied heavily on pre-training and information regarding the building or users beforehand. Their work can generalize well to many types of tall buildings which are more than 19 stories. Another benefit to their system is that they don't need any additional infrastructure support in advance making it a practical solution for deployment. <br />
<br />
With rising number of smartphone users, cellular network capacity is reaching its limits and not able to cater to multiple users. One of the major concerns being the indoor cellular coverage and seamless mobility between indoor-outdoor cellular networks. The proposed solution can enable in providing this connectivity between cells for example handover between an indoor pico/nano cell, Wi-Fi network to an outdoor macro cell network; moreover with the floor detection algorithm, connectivity can be improved for users under low coverage areas such as basements, underground car parking, etc. Hence this can be integrated into one of the 5G use cases for improved network coverage. <br />
<br />
A weakness is that they claim they can get 100% accuracy, but this is only if they know the floor to ceiling height, and their accuracy relies on this key piece of information. Otherwise, when conditioned on the height of the building their accuracy drops by 35% to 65%. Also, the article's ideas are sometimes out of order and are repeated in cycles.<br />
<br />
It is also not clear that the LSTM is the best approach especially since a simple feedforward network achieved the same accuracy in their experiments.<br />
<br />
They also go against their claim stated at the beginning of the paper where they say they "..does not require the use of beacons, prior knowledge of the building infrastructure..." as in their clustering step they are in a way using prior knowledge from previous visits [4].<br />
<br />
The authors also recognize several potential failings of their method. One is that their algorithm will not differentiate based on the floor of the building the user entered on (if there are entrances on multiple floors). In addition, they state that a user on the roof could be detected as being on the ground floor. It was not mentioned/explored in the paper, but a person being on a balcony (ex: attached to an apartment) may have the same effect. These sources of error will need to be corrected before this or a similar algorithm is implemented; otherwise, the algorithm may provide the misleading data to rescue crews, etc.<br />
<br />
Overall this paper is not too novel, as they don't provide any algorithmic improvement over the state of the art. Their methods are fairly standard ML techniques and they have only used out of the box solutions. There is no clear intuition why the proposed work well for the authors. This application could be solved using simpler methods like having an emergency push button on each floor. Moreover, authors don't provide sufficient motivation for why deep learning would be a good solution to this problem.<br />
<br />
The proposed model could introduce privacy risks such as illegal surveillance of mobile phone user and private facilities.<br />
<br />
=References=<br />
<br />
[1] Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural Computation, 9(8):<br />
1735–1780, 1997.<br />
<br />
[2] Parnandi, A., Le, K., Vaghela, P., Kolli, A., Dantu, K., Poduri, S., & Sukhatme, G. S. (2009, October). Coarse in-building localization with smartphones. In International Conference on Mobile Computing, Applications, and Services (pp. 343-354). Springer, Berlin, Heidelberg.<br />
<br />
[3] Wonsang Song, Jae Woo Lee, Byung Suk Lee, Henning Schulzrinne. "Finding 9-1-1 Callers in Tall Buildings". IEEE WoWMoM '14. Sydney, Australia, June 2014.<br />
<br />
[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and Smartphone Sensor Data, 2018<br />
<br />
[5] Kawakubo, Hideko and Hiroaki Yoshida. “Rapid Feature Selection Based on Random Forests for High-Dimensional Data.” (2012).<br />
<br />
[6] James Bergstra and Yoshua Bengio. 2012. Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13 (February 2012), 281-305.<br />
<br />
[7] Greg Milette, Adam Stroud: Professional Android Sensor Programming, 2012, Wiley India</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data&diff=42236Predicting Floor Level For 911 Calls with Neural Network and Smartphone Sensor Data2018-12-03T03:58:29Z<p>A22ravi: /* Critique */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
In highly populated cities with many buildings, locating individuals in the case of an emergency is an important task. For emergency responders, time is of essence. Therefore, accurately locating a 911 caller plays an integral role in this important process.<br />
<br />
The motivation for this problem is in the context of 911 calls: victims trapped in a tall building who seek immediate medical attention, locating emergency personnel such as firefighters or paramedics, or a minor calling on behalf of an incapacitated adult. <br />
<br />
In this paper, a novel approach is presented to accurately predict floor level for 911 calls by leveraging neural networks and sensor data from smartphones.<br />
<br />
In large cities with tall buildings, relying on GPS or Wi-Fi signals does not always lead to an accurate location of a caller.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:17floor.png|250px]]<br />
[[File:19floor.png|250px]]</div><br />
<br />
<br />
In this work, there are two major contributions. The first is that they trained a LSTM to classify whether a smartphone was either inside or outside a building using GPS, Received signal strength indication (RSSI), and magnetometer sensor readings. The model is compared with baseline models like feed-forward neural networks, logistic regression, SVM, HMM, and Random Forests. The second contribution is an algorithm, which uses the output of the trained LSTM, to predict change in the barometric pressure of the smartphone from when it first entered the building against that of its current location within the building. In the final part of their algorithm, they are able to predict the floor level by clustering the measurements of height.<br />
<br />
The model does not rely on the external sensors placed inside the building, prior knowledge of the building, nor user movement behaviour. The only input it looks at is the GPS and the barometric signal from the phone. Finally, they also talk about the application of this algorithm in a variety of other real-world situations. <br />
<br />
All the codes and data related to this article are available here[[https://github.com/williamFalcon/Predicting-floor-level-for-911-Calls-with-Neural-Networks-and-Smartphone-Sensor-Data]]<br />
<br />
=Related Work=<br />
<br />
<br />
In general, previous work falls under two categories. The first category of methods is the classification methods based on the user's activity. <br />
Therefore, some current methods leverage the user's activity to predict which is based on the offset in their movement [2]. These activities include running, walking, and moving through the elevator.<br />
The second set of methods focus more on the use of a barometer which measures the atmospheric pressure. As a result, utilizing a barometer can provide the changes in altitude.<br />
<br />
Avinash Parnandi and his coauthors used multiple classifiers in the predicting the floor level [2]. The steps in their algorithmic process are: <br />
<ol><br />
<li> Classifier to predict whether the user is indoors or outdoors</li><br />
<li> Classifier to identify if the activity of the user, i.e. walking, standing still etc. </li><br />
<li> Classifier to measure the displacement</li><br />
</ol><br />
<br />
One of the downsides of this work is to achieve the high accuracy that the user's step size is needed, therefore heavily relying on pre-training to the specific users. In a real world application of this method, this would not be practical.<br />
<br />
<br />
Song and his colleagues model the way or cause of ascent. That is, was the ascent a result of taking the elevator, stairs or escalator [3]. Then by using infrastructure support of the buildings and as well as additional tuning they are able to predict floor level. <br />
This method also suffers from relying on data specific to the building. <br />
<br />
Overall, these methods suffer from relying on pre-training to a specific user, needing additional infrastructure support, or data specific to the building. The method proposed in this paper aims to predict floor level without these constraints.<br />
<br />
=Method=<br />
<br />
<br />
In their paper, the authors claim that to their knowledge "there does not exist a dataset for predicting floor heights" [4].<br />
<br />
To collect data, the authors developed an iOS application (called Sensory) that runs on an iPhone 6s to aggregate the data. They used the smartphone's sensors to record different features such as barometric pressure, GPS course, GPS speed, RSSI strength, GPS longitude, GPS latitude, and altitude. The app streamed data at 1 sample per second, and each datum contained the different sensor measurements mentions earlier along with environment contexts like building floors, environment activity, city name, country name, and magnetic strength.<br />
<br />
The data collection procedure for '''indoor-outdoor classifier''' was described as follows:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) As soon as we exit, set indoors to 0. 7) Stop recording. 8) Save data as CSV for analysis. This procedure can start either outside or inside a building without loss of generality.<br />
<br />
The following procedure generates data used to '''predict a floor change''' from the entrance floor to the end floor:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) Finally, enter a building and ascend/descend to any story. 7) Ascend through any method desired, stairs, elevator, escalator, etc. 8) Once at the floor, stop recording. 9) Save data as CSV for analysis.<br />
<br />
Their algorithm was used to predict floor level which is a 3 part process:<br />
<br />
<ol><br />
<li> Classifying whether smartphone is indoor or outdoor </li><br />
<li> Indoor/Outdoor Transition detector</li><br />
<li> Estimating vertical height and resolving to absolute floor level </li><br />
</ol><br />
<br />
==1) Classifying Indoor/Outdoor ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:classifierfloor.png|800px]] </div><br />
<br />
From [5] they are using 6 features which were found through forests of trees feature reduction. The features are smartphone's barometric pressure (<math>P</math>), GPS vertical accuracy (<math>GV</math>), GPS horizontal accuracy (<math>GH</math>), GPS speed (<math>S</math>), device RSSI level (<math>rssi</math>), and magnetometer total reading (<math>M</math>).<br />
<br />
The magnetometer total reading was calculated from given the 3-dimensional reading <math>x, y, z </math><br />
<br />
<br />
<div style="text-align: center;">Total Magnetic field strength <math>= M = \sqrt{x^{2} + y^{2} + z^{2}}</math></div><br />
<br />
They used a 3 layer LSTM where the inputs are <math> d </math> consecutive time steps. The output <math> y = 1 </math> if smartphone is indoor and <math> y = 0 </math> if smartphone is outdoor.<br />
<br />
In their design they set <math> d = 3</math> by random search [6]. The point to make is that they wanted the network to learn the relationship given a little bit of information from both the past and future.<br />
<br />
For the overall signal sequence: <math> \{x_1, x_2,x_j, ... , x_n\}</math> the aim is to classify <math> d </math> consecutive sensor readings <math> X_i = \{x_1, x_2, ..., x_d \} </math> as <math> y = 1 </math> or <math> y = 0 </math> as noted above.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Table5.png|750px]] </div><br />
<br />
This is a critical part of their system and they only focus on the predictions in the subspace of being indoors. <br />
<br />
They have trained the LSTM to minimize the binary cross entropy between the true indoor state <math> y </math> of example <math> i </math>. <br />
<br />
The cost function is shown below:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:costfunction.png|450px]] </div><br />
<br />
The final output of the LSTM is a time-series <math> T = {t_1, t_2, ..., t_i, t_n} </math> where each <math> t_i = 0, t_i = 1 </math> if the point is outside or inside respectively.<br />
<br />
==2) Transition Detector ==<br />
<br />
Given the predictions from the previous step, now the next part is to find when the transition of going in or out of a building has occurred.<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:transition.png|400px]] </div><br />
In this figure, they convolve filters <math> V_1, V_2</math> across the predictions T and they pick a subset <math>s_i </math> such that the Jacard distance (defined below) is <math> >= 0.4 </math><br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:v1v2.png|250px]] </div><br />
Jacard Distance:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:jacard.png|450px]]</div><br />
<br />
After this process, we are now left with a set of <math> b_i</math>'s describing the index of each indoor/outdoor transition. The process is shown in the first figure.<br />
<br />
==3) Vertical height and floor level ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:resolvefloor.png|700px]] </div><br />
<br />
[3] suggested the use of a reference barometer or beacons as a way to determine the entrances to a building.<br />
<br />
However, such need is eliminated by the authors' approach. The authors' second key contribution is to use the LSTM IO predictions to help identifying these indoor transitions into the building. The LSTM provides a self-contained estimator of a building’s entrance without relying on external sensor information on a user’s body or beacons placed inside a building’s lobby. [4]<br />
<br />
In the final part of the system, the vertical offset needs to be computed given the smartphone's last known location i.e. the last known transition which can easily be computed given the set of transitions from the previous step. All that needs to be done is to pull the index of most recent transition from the previous step and set <math> p_0</math> to the lowest pressure within a ~ 15-second window around that index.<br />
<br />
The second parameter is <math> p_1 </math> which is the current pressure reading. In order to generate the relative change in height <math> m_\Delta</math><br />
<br />
After plugging this into the formula defined above we are now left with a scalar value which represents the height displacement between the entrance and the smartphone's current location of the building [7].<br />
<br />
In order to resolve to an absolute floor level, they use the index number of the clusters of <math> m_\Delta</math> 's. As seen above <math> 5.1 </math> is the third cluster implying floor number 3.<br />
<br />
=Experiments and Results=<br />
<br />
==Dataset==<br />
<br />
In this paper, an iOS app called Sensory is developed which is used to collect data on an iPhone 6. The following sensor readings were recorded: '''indoors''', '''created at''', '''session id''', '''floor''', '''RSSI strength''', '''GPS latitude''', '''GPS longitude''', '''GPS vertical accuracy''', '''GPS horizontal accuracy''', '''GPS course''', '''GPS speed''', '''barometric relative altitude''', '''barometric pressure''', '''environment context''', '''environment mean building floors''', '''environment activity''', '''city name''', '''country name''', '''magnet x''', '''magnet y''', '''magnet z''', '''magnet total'''.<br />
<br />
As soon as the user enters or exits a building, the indoor-outdoor data has to be manually entered. To gather the data for the floor level prediction, the authors conducted 63 trials among five different buildings throughout New York City. Since unsupervised learning was being used, the actual floor level was recorded manually for the validation purposes only.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:ioaccuracy.png|450px]] </div><br />
<br />
All of these classifiers were trained and validated on data from a total of 5082 data points. The set split was 80% training and 20% validation. <br />
For the LSTM the network was trained for a total of 24 epochs with a batch size of 128 and using an Adam optimizer where the learning rate was 0.006. <br />
Although the baselines performed considerably well the objective here was to show that an LSTM can be used in the future to model the entire system with an LSTM.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:flooraccuracy.png|650px]] </div><br />
<br />
The above chart shows the success that their system is able to achieve in the floor level prediction.<br />
<br />
The performance was measured in terms of how many floors were travelled rather than the absolute floor number. Because different buildings might have their floors differently numbered. They used different m values in 2 tests. One applies the same m value across all building and the other one applied specific m values on different buildings. The result showed that this specification on m values hugely increased the accuracy.<br />
<br />
=Future Work=<br />
The first part of the system used an LSTM for indoor/outdoor classification. Therefore, this separate module can be used in many other location problems. Working on this separate problem seems to be an approach that the authors will take. They also would like to aim towards modeling the whole problem within the LSTM in order to generate the floor level predictions solely from sensor reading data.<br />
<br />
=Critique=<br />
<br />
In this paper, the authors presented a novel system which can predict a smartphone's floor level with 100% accuracy, which has not been done. Previous work relied heavily on pre-training and information regarding the building or users beforehand. Their work can generalize well to many types of tall buildings which are more than 19 stories. Another benefit to their system is that they don't need any additional infrastructure support in advance making it a practical solution for deployment. <br />
<br />
With rising number of smartphone users, cellular network capacity is reaching its limits and not able to cater to multiple users. One of the major concerns being the indoor cellular coverage and seamless mobility between indoor-outdoor cellular networks. The proposed solution can enable in providing this connectivity between cells for example handover between an indoor pico/nano cell, Wi-Fi network to an outdoor macro cell network; moreover with the floor detection algorithm, connectivity can be improved for users under low coverage areas such as basements, underground car parking, etc. <br />
<br />
A weakness is that they claim they can get 100% accuracy, but this is only if they know the floor to ceiling height, and their accuracy relies on this key piece of information. Otherwise, when conditioned on the height of the building their accuracy drops by 35% to 65%. Also, the article's ideas are sometimes out of order and are repeated in cycles.<br />
<br />
It is also not clear that the LSTM is the best approach especially since a simple feedforward network achieved the same accuracy in their experiments.<br />
<br />
They also go against their claim stated at the beginning of the paper where they say they "..does not require the use of beacons, prior knowledge of the building infrastructure..." as in their clustering step they are in a way using prior knowledge from previous visits [4].<br />
<br />
The authors also recognize several potential failings of their method. One is that their algorithm will not differentiate based on the floor of the building the user entered on (if there are entrances on multiple floors). In addition, they state that a user on the roof could be detected as being on the ground floor. It was not mentioned/explored in the paper, but a person being on a balcony (ex: attached to an apartment) may have the same effect. These sources of error will need to be corrected before this or a similar algorithm is implemented; otherwise, the algorithm may provide the misleading data to rescue crews, etc.<br />
<br />
Overall this paper is not too novel, as they don't provide any algorithmic improvement over the state of the art. Their methods are fairly standard ML techniques and they have only used out of the box solutions. There is no clear intuition why the proposed work well for the authors. This application could be solved using simpler methods like having an emergency push button on each floor. Moreover, authors don't provide sufficient motivation for why deep learning would be a good solution to this problem.<br />
<br />
The proposed model could introduce privacy risks such as illegal surveillance of mobile phone user and private facilities.<br />
<br />
=References=<br />
<br />
[1] Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural Computation, 9(8):<br />
1735–1780, 1997.<br />
<br />
[2] Parnandi, A., Le, K., Vaghela, P., Kolli, A., Dantu, K., Poduri, S., & Sukhatme, G. S. (2009, October). Coarse in-building localization with smartphones. In International Conference on Mobile Computing, Applications, and Services (pp. 343-354). Springer, Berlin, Heidelberg.<br />
<br />
[3] Wonsang Song, Jae Woo Lee, Byung Suk Lee, Henning Schulzrinne. "Finding 9-1-1 Callers in Tall Buildings". IEEE WoWMoM '14. Sydney, Australia, June 2014.<br />
<br />
[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and Smartphone Sensor Data, 2018<br />
<br />
[5] Kawakubo, Hideko and Hiroaki Yoshida. “Rapid Feature Selection Based on Random Forests for High-Dimensional Data.” (2012).<br />
<br />
[6] James Bergstra and Yoshua Bengio. 2012. Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13 (February 2012), 281-305.<br />
<br />
[7] Greg Milette, Adam Stroud: Professional Android Sensor Programming, 2012, Wiley India</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data&diff=42235Predicting Floor Level For 911 Calls with Neural Network and Smartphone Sensor Data2018-12-03T03:57:31Z<p>A22ravi: /* Critique */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
In highly populated cities with many buildings, locating individuals in the case of an emergency is an important task. For emergency responders, time is of essence. Therefore, accurately locating a 911 caller plays an integral role in this important process.<br />
<br />
The motivation for this problem is in the context of 911 calls: victims trapped in a tall building who seek immediate medical attention, locating emergency personnel such as firefighters or paramedics, or a minor calling on behalf of an incapacitated adult. <br />
<br />
In this paper, a novel approach is presented to accurately predict floor level for 911 calls by leveraging neural networks and sensor data from smartphones.<br />
<br />
In large cities with tall buildings, relying on GPS or Wi-Fi signals does not always lead to an accurate location of a caller.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:17floor.png|250px]]<br />
[[File:19floor.png|250px]]</div><br />
<br />
<br />
In this work, there are two major contributions. The first is that they trained a LSTM to classify whether a smartphone was either inside or outside a building using GPS, Received signal strength indication (RSSI), and magnetometer sensor readings. The model is compared with baseline models like feed-forward neural networks, logistic regression, SVM, HMM, and Random Forests. The second contribution is an algorithm, which uses the output of the trained LSTM, to predict change in the barometric pressure of the smartphone from when it first entered the building against that of its current location within the building. In the final part of their algorithm, they are able to predict the floor level by clustering the measurements of height.<br />
<br />
The model does not rely on the external sensors placed inside the building, prior knowledge of the building, nor user movement behaviour. The only input it looks at is the GPS and the barometric signal from the phone. Finally, they also talk about the application of this algorithm in a variety of other real-world situations. <br />
<br />
All the codes and data related to this article are available here[[https://github.com/williamFalcon/Predicting-floor-level-for-911-Calls-with-Neural-Networks-and-Smartphone-Sensor-Data]]<br />
<br />
=Related Work=<br />
<br />
<br />
In general, previous work falls under two categories. The first category of methods is the classification methods based on the user's activity. <br />
Therefore, some current methods leverage the user's activity to predict which is based on the offset in their movement [2]. These activities include running, walking, and moving through the elevator.<br />
The second set of methods focus more on the use of a barometer which measures the atmospheric pressure. As a result, utilizing a barometer can provide the changes in altitude.<br />
<br />
Avinash Parnandi and his coauthors used multiple classifiers in the predicting the floor level [2]. The steps in their algorithmic process are: <br />
<ol><br />
<li> Classifier to predict whether the user is indoors or outdoors</li><br />
<li> Classifier to identify if the activity of the user, i.e. walking, standing still etc. </li><br />
<li> Classifier to measure the displacement</li><br />
</ol><br />
<br />
One of the downsides of this work is to achieve the high accuracy that the user's step size is needed, therefore heavily relying on pre-training to the specific users. In a real world application of this method, this would not be practical.<br />
<br />
<br />
Song and his colleagues model the way or cause of ascent. That is, was the ascent a result of taking the elevator, stairs or escalator [3]. Then by using infrastructure support of the buildings and as well as additional tuning they are able to predict floor level. <br />
This method also suffers from relying on data specific to the building. <br />
<br />
Overall, these methods suffer from relying on pre-training to a specific user, needing additional infrastructure support, or data specific to the building. The method proposed in this paper aims to predict floor level without these constraints.<br />
<br />
=Method=<br />
<br />
<br />
In their paper, the authors claim that to their knowledge "there does not exist a dataset for predicting floor heights" [4].<br />
<br />
To collect data, the authors developed an iOS application (called Sensory) that runs on an iPhone 6s to aggregate the data. They used the smartphone's sensors to record different features such as barometric pressure, GPS course, GPS speed, RSSI strength, GPS longitude, GPS latitude, and altitude. The app streamed data at 1 sample per second, and each datum contained the different sensor measurements mentions earlier along with environment contexts like building floors, environment activity, city name, country name, and magnetic strength.<br />
<br />
The data collection procedure for '''indoor-outdoor classifier''' was described as follows:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) As soon as we exit, set indoors to 0. 7) Stop recording. 8) Save data as CSV for analysis. This procedure can start either outside or inside a building without loss of generality.<br />
<br />
The following procedure generates data used to '''predict a floor change''' from the entrance floor to the end floor:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) Finally, enter a building and ascend/descend to any story. 7) Ascend through any method desired, stairs, elevator, escalator, etc. 8) Once at the floor, stop recording. 9) Save data as CSV for analysis.<br />
<br />
Their algorithm was used to predict floor level which is a 3 part process:<br />
<br />
<ol><br />
<li> Classifying whether smartphone is indoor or outdoor </li><br />
<li> Indoor/Outdoor Transition detector</li><br />
<li> Estimating vertical height and resolving to absolute floor level </li><br />
</ol><br />
<br />
==1) Classifying Indoor/Outdoor ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:classifierfloor.png|800px]] </div><br />
<br />
From [5] they are using 6 features which were found through forests of trees feature reduction. The features are smartphone's barometric pressure (<math>P</math>), GPS vertical accuracy (<math>GV</math>), GPS horizontal accuracy (<math>GH</math>), GPS speed (<math>S</math>), device RSSI level (<math>rssi</math>), and magnetometer total reading (<math>M</math>).<br />
<br />
The magnetometer total reading was calculated from given the 3-dimensional reading <math>x, y, z </math><br />
<br />
<br />
<div style="text-align: center;">Total Magnetic field strength <math>= M = \sqrt{x^{2} + y^{2} + z^{2}}</math></div><br />
<br />
They used a 3 layer LSTM where the inputs are <math> d </math> consecutive time steps. The output <math> y = 1 </math> if smartphone is indoor and <math> y = 0 </math> if smartphone is outdoor.<br />
<br />
In their design they set <math> d = 3</math> by random search [6]. The point to make is that they wanted the network to learn the relationship given a little bit of information from both the past and future.<br />
<br />
For the overall signal sequence: <math> \{x_1, x_2,x_j, ... , x_n\}</math> the aim is to classify <math> d </math> consecutive sensor readings <math> X_i = \{x_1, x_2, ..., x_d \} </math> as <math> y = 1 </math> or <math> y = 0 </math> as noted above.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Table5.png|750px]] </div><br />
<br />
This is a critical part of their system and they only focus on the predictions in the subspace of being indoors. <br />
<br />
They have trained the LSTM to minimize the binary cross entropy between the true indoor state <math> y </math> of example <math> i </math>. <br />
<br />
The cost function is shown below:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:costfunction.png|450px]] </div><br />
<br />
The final output of the LSTM is a time-series <math> T = {t_1, t_2, ..., t_i, t_n} </math> where each <math> t_i = 0, t_i = 1 </math> if the point is outside or inside respectively.<br />
<br />
==2) Transition Detector ==<br />
<br />
Given the predictions from the previous step, now the next part is to find when the transition of going in or out of a building has occurred.<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:transition.png|400px]] </div><br />
In this figure, they convolve filters <math> V_1, V_2</math> across the predictions T and they pick a subset <math>s_i </math> such that the Jacard distance (defined below) is <math> >= 0.4 </math><br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:v1v2.png|250px]] </div><br />
Jacard Distance:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:jacard.png|450px]]</div><br />
<br />
After this process, we are now left with a set of <math> b_i</math>'s describing the index of each indoor/outdoor transition. The process is shown in the first figure.<br />
<br />
==3) Vertical height and floor level ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:resolvefloor.png|700px]] </div><br />
<br />
[3] suggested the use of a reference barometer or beacons as a way to determine the entrances to a building.<br />
<br />
However, such need is eliminated by the authors' approach. The authors' second key contribution is to use the LSTM IO predictions to help identifying these indoor transitions into the building. The LSTM provides a self-contained estimator of a building’s entrance without relying on external sensor information on a user’s body or beacons placed inside a building’s lobby. [4]<br />
<br />
In the final part of the system, the vertical offset needs to be computed given the smartphone's last known location i.e. the last known transition which can easily be computed given the set of transitions from the previous step. All that needs to be done is to pull the index of most recent transition from the previous step and set <math> p_0</math> to the lowest pressure within a ~ 15-second window around that index.<br />
<br />
The second parameter is <math> p_1 </math> which is the current pressure reading. In order to generate the relative change in height <math> m_\Delta</math><br />
<br />
After plugging this into the formula defined above we are now left with a scalar value which represents the height displacement between the entrance and the smartphone's current location of the building [7].<br />
<br />
In order to resolve to an absolute floor level, they use the index number of the clusters of <math> m_\Delta</math> 's. As seen above <math> 5.1 </math> is the third cluster implying floor number 3.<br />
<br />
=Experiments and Results=<br />
<br />
==Dataset==<br />
<br />
In this paper, an iOS app called Sensory is developed which is used to collect data on an iPhone 6. The following sensor readings were recorded: '''indoors''', '''created at''', '''session id''', '''floor''', '''RSSI strength''', '''GPS latitude''', '''GPS longitude''', '''GPS vertical accuracy''', '''GPS horizontal accuracy''', '''GPS course''', '''GPS speed''', '''barometric relative altitude''', '''barometric pressure''', '''environment context''', '''environment mean building floors''', '''environment activity''', '''city name''', '''country name''', '''magnet x''', '''magnet y''', '''magnet z''', '''magnet total'''.<br />
<br />
As soon as the user enters or exits a building, the indoor-outdoor data has to be manually entered. To gather the data for the floor level prediction, the authors conducted 63 trials among five different buildings throughout New York City. Since unsupervised learning was being used, the actual floor level was recorded manually for the validation purposes only.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:ioaccuracy.png|450px]] </div><br />
<br />
All of these classifiers were trained and validated on data from a total of 5082 data points. The set split was 80% training and 20% validation. <br />
For the LSTM the network was trained for a total of 24 epochs with a batch size of 128 and using an Adam optimizer where the learning rate was 0.006. <br />
Although the baselines performed considerably well the objective here was to show that an LSTM can be used in the future to model the entire system with an LSTM.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:flooraccuracy.png|650px]] </div><br />
<br />
The above chart shows the success that their system is able to achieve in the floor level prediction.<br />
<br />
The performance was measured in terms of how many floors were travelled rather than the absolute floor number. Because different buildings might have their floors differently numbered. They used different m values in 2 tests. One applies the same m value across all building and the other one applied specific m values on different buildings. The result showed that this specification on m values hugely increased the accuracy.<br />
<br />
=Future Work=<br />
The first part of the system used an LSTM for indoor/outdoor classification. Therefore, this separate module can be used in many other location problems. Working on this separate problem seems to be an approach that the authors will take. They also would like to aim towards modeling the whole problem within the LSTM in order to generate the floor level predictions solely from sensor reading data.<br />
<br />
=Critique=<br />
<br />
In this paper, the authors presented a novel system which can predict a smartphone's floor level with 100% accuracy, which has not been done. Previous work relied heavily on pre-training and information regarding the building or users beforehand. Their work can generalize well to many types of tall buildings which are more than 19 stories. Another benefit to their system is that they don't need any additional infrastructure support in advance making it a practical solution for deployment. <br />
<br />
With rising number of smartphone users, cellular network capacity is reaching its limits and not able to cater to multiple users. One of the major concerns being the indoor cellular coverage and seamless mobility between indoor-outdoor cellular networks. The proposed solution can enable in providing this connectivity between cells for example handover between an indoor pico/nano cell to an outdoor macro cell network; moreover with the floor detection algorithm, connectivity can be improved for users under low coverage areas such as basements, underground car parking, etc. <br />
<br />
A weakness is that they claim they can get 100% accuracy, but this is only if they know the floor to ceiling height, and their accuracy relies on this key piece of information. Otherwise, when conditioned on the height of the building their accuracy drops by 35% to 65%. Also, the article's ideas are sometimes out of order and are repeated in cycles.<br />
<br />
It is also not clear that the LSTM is the best approach especially since a simple feedforward network achieved the same accuracy in their experiments.<br />
<br />
They also go against their claim stated at the beginning of the paper where they say they "..does not require the use of beacons, prior knowledge of the building infrastructure..." as in their clustering step they are in a way using prior knowledge from previous visits [4].<br />
<br />
The authors also recognize several potential failings of their method. One is that their algorithm will not differentiate based on the floor of the building the user entered on (if there are entrances on multiple floors). In addition, they state that a user on the roof could be detected as being on the ground floor. It was not mentioned/explored in the paper, but a person being on a balcony (ex: attached to an apartment) may have the same effect. These sources of error will need to be corrected before this or a similar algorithm is implemented; otherwise, the algorithm may provide the misleading data to rescue crews, etc.<br />
<br />
Overall this paper is not too novel, as they don't provide any algorithmic improvement over the state of the art. Their methods are fairly standard ML techniques and they have only used out of the box solutions. There is no clear intuition why the proposed work well for the authors. This application could be solved using simpler methods like having an emergency push button on each floor. Moreover, authors don't provide sufficient motivation for why deep learning would be a good solution to this problem.<br />
<br />
The proposed model could introduce privacy risks such as illegal surveillance of mobile phone user and private facilities.<br />
<br />
=References=<br />
<br />
[1] Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural Computation, 9(8):<br />
1735–1780, 1997.<br />
<br />
[2] Parnandi, A., Le, K., Vaghela, P., Kolli, A., Dantu, K., Poduri, S., & Sukhatme, G. S. (2009, October). Coarse in-building localization with smartphones. In International Conference on Mobile Computing, Applications, and Services (pp. 343-354). Springer, Berlin, Heidelberg.<br />
<br />
[3] Wonsang Song, Jae Woo Lee, Byung Suk Lee, Henning Schulzrinne. "Finding 9-1-1 Callers in Tall Buildings". IEEE WoWMoM '14. Sydney, Australia, June 2014.<br />
<br />
[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and Smartphone Sensor Data, 2018<br />
<br />
[5] Kawakubo, Hideko and Hiroaki Yoshida. “Rapid Feature Selection Based on Random Forests for High-Dimensional Data.” (2012).<br />
<br />
[6] James Bergstra and Yoshua Bengio. 2012. Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13 (February 2012), 281-305.<br />
<br />
[7] Greg Milette, Adam Stroud: Professional Android Sensor Programming, 2012, Wiley India</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data&diff=42234Predicting Floor Level For 911 Calls with Neural Network and Smartphone Sensor Data2018-12-03T03:46:24Z<p>A22ravi: /* Method */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
In highly populated cities with many buildings, locating individuals in the case of an emergency is an important task. For emergency responders, time is of essence. Therefore, accurately locating a 911 caller plays an integral role in this important process.<br />
<br />
The motivation for this problem is in the context of 911 calls: victims trapped in a tall building who seek immediate medical attention, locating emergency personnel such as firefighters or paramedics, or a minor calling on behalf of an incapacitated adult. <br />
<br />
In this paper, a novel approach is presented to accurately predict floor level for 911 calls by leveraging neural networks and sensor data from smartphones.<br />
<br />
In large cities with tall buildings, relying on GPS or Wi-Fi signals does not always lead to an accurate location of a caller.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:17floor.png|250px]]<br />
[[File:19floor.png|250px]]</div><br />
<br />
<br />
In this work, there are two major contributions. The first is that they trained a LSTM to classify whether a smartphone was either inside or outside a building using GPS, Received signal strength indication (RSSI), and magnetometer sensor readings. The model is compared with baseline models like feed-forward neural networks, logistic regression, SVM, HMM, and Random Forests. The second contribution is an algorithm, which uses the output of the trained LSTM, to predict change in the barometric pressure of the smartphone from when it first entered the building against that of its current location within the building. In the final part of their algorithm, they are able to predict the floor level by clustering the measurements of height.<br />
<br />
The model does not rely on the external sensors placed inside the building, prior knowledge of the building, nor user movement behaviour. The only input it looks at is the GPS and the barometric signal from the phone. Finally, they also talk about the application of this algorithm in a variety of other real-world situations. <br />
<br />
All the codes and data related to this article are available here[[https://github.com/williamFalcon/Predicting-floor-level-for-911-Calls-with-Neural-Networks-and-Smartphone-Sensor-Data]]<br />
<br />
=Related Work=<br />
<br />
<br />
In general, previous work falls under two categories. The first category of methods is the classification methods based on the user's activity. <br />
Therefore, some current methods leverage the user's activity to predict which is based on the offset in their movement [2]. These activities include running, walking, and moving through the elevator.<br />
The second set of methods focus more on the use of a barometer which measures the atmospheric pressure. As a result, utilizing a barometer can provide the changes in altitude.<br />
<br />
Avinash Parnandi and his coauthors used multiple classifiers in the predicting the floor level [2]. The steps in their algorithmic process are: <br />
<ol><br />
<li> Classifier to predict whether the user is indoors or outdoors</li><br />
<li> Classifier to identify if the activity of the user, i.e. walking, standing still etc. </li><br />
<li> Classifier to measure the displacement</li><br />
</ol><br />
<br />
One of the downsides of this work is to achieve the high accuracy that the user's step size is needed, therefore heavily relying on pre-training to the specific users. In a real world application of this method, this would not be practical.<br />
<br />
<br />
Song and his colleagues model the way or cause of ascent. That is, was the ascent a result of taking the elevator, stairs or escalator [3]. Then by using infrastructure support of the buildings and as well as additional tuning they are able to predict floor level. <br />
This method also suffers from relying on data specific to the building. <br />
<br />
Overall, these methods suffer from relying on pre-training to a specific user, needing additional infrastructure support, or data specific to the building. The method proposed in this paper aims to predict floor level without these constraints.<br />
<br />
=Method=<br />
<br />
<br />
In their paper, the authors claim that to their knowledge "there does not exist a dataset for predicting floor heights" [4].<br />
<br />
To collect data, the authors developed an iOS application (called Sensory) that runs on an iPhone 6s to aggregate the data. They used the smartphone's sensors to record different features such as barometric pressure, GPS course, GPS speed, RSSI strength, GPS longitude, GPS latitude, and altitude. The app streamed data at 1 sample per second, and each datum contained the different sensor measurements mentions earlier along with environment contexts like building floors, environment activity, city name, country name, and magnetic strength.<br />
<br />
The data collection procedure for '''indoor-outdoor classifier''' was described as follows:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) As soon as we exit, set indoors to 0. 7) Stop recording. 8) Save data as CSV for analysis. This procedure can start either outside or inside a building without loss of generality.<br />
<br />
The following procedure generates data used to '''predict a floor change''' from the entrance floor to the end floor:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) Finally, enter a building and ascend/descend to any story. 7) Ascend through any method desired, stairs, elevator, escalator, etc. 8) Once at the floor, stop recording. 9) Save data as CSV for analysis.<br />
<br />
Their algorithm was used to predict floor level which is a 3 part process:<br />
<br />
<ol><br />
<li> Classifying whether smartphone is indoor or outdoor </li><br />
<li> Indoor/Outdoor Transition detector</li><br />
<li> Estimating vertical height and resolving to absolute floor level </li><br />
</ol><br />
<br />
==1) Classifying Indoor/Outdoor ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:classifierfloor.png|800px]] </div><br />
<br />
From [5] they are using 6 features which were found through forests of trees feature reduction. The features are smartphone's barometric pressure (<math>P</math>), GPS vertical accuracy (<math>GV</math>), GPS horizontal accuracy (<math>GH</math>), GPS speed (<math>S</math>), device RSSI level (<math>rssi</math>), and magnetometer total reading (<math>M</math>).<br />
<br />
The magnetometer total reading was calculated from given the 3-dimensional reading <math>x, y, z </math><br />
<br />
<br />
<div style="text-align: center;">Total Magnetic field strength <math>= M = \sqrt{x^{2} + y^{2} + z^{2}}</math></div><br />
<br />
They used a 3 layer LSTM where the inputs are <math> d </math> consecutive time steps. The output <math> y = 1 </math> if smartphone is indoor and <math> y = 0 </math> if smartphone is outdoor.<br />
<br />
In their design they set <math> d = 3</math> by random search [6]. The point to make is that they wanted the network to learn the relationship given a little bit of information from both the past and future.<br />
<br />
For the overall signal sequence: <math> \{x_1, x_2,x_j, ... , x_n\}</math> the aim is to classify <math> d </math> consecutive sensor readings <math> X_i = \{x_1, x_2, ..., x_d \} </math> as <math> y = 1 </math> or <math> y = 0 </math> as noted above.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Table5.png|750px]] </div><br />
<br />
This is a critical part of their system and they only focus on the predictions in the subspace of being indoors. <br />
<br />
They have trained the LSTM to minimize the binary cross entropy between the true indoor state <math> y </math> of example <math> i </math>. <br />
<br />
The cost function is shown below:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:costfunction.png|450px]] </div><br />
<br />
The final output of the LSTM is a time-series <math> T = {t_1, t_2, ..., t_i, t_n} </math> where each <math> t_i = 0, t_i = 1 </math> if the point is outside or inside respectively.<br />
<br />
==2) Transition Detector ==<br />
<br />
Given the predictions from the previous step, now the next part is to find when the transition of going in or out of a building has occurred.<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:transition.png|400px]] </div><br />
In this figure, they convolve filters <math> V_1, V_2</math> across the predictions T and they pick a subset <math>s_i </math> such that the Jacard distance (defined below) is <math> >= 0.4 </math><br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:v1v2.png|250px]] </div><br />
Jacard Distance:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:jacard.png|450px]]</div><br />
<br />
After this process, we are now left with a set of <math> b_i</math>'s describing the index of each indoor/outdoor transition. The process is shown in the first figure.<br />
<br />
==3) Vertical height and floor level ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:resolvefloor.png|700px]] </div><br />
<br />
[3] suggested the use of a reference barometer or beacons as a way to determine the entrances to a building.<br />
<br />
However, such need is eliminated by the authors' approach. The authors' second key contribution is to use the LSTM IO predictions to help identifying these indoor transitions into the building. The LSTM provides a self-contained estimator of a building’s entrance without relying on external sensor information on a user’s body or beacons placed inside a building’s lobby. [4]<br />
<br />
In the final part of the system, the vertical offset needs to be computed given the smartphone's last known location i.e. the last known transition which can easily be computed given the set of transitions from the previous step. All that needs to be done is to pull the index of most recent transition from the previous step and set <math> p_0</math> to the lowest pressure within a ~ 15-second window around that index.<br />
<br />
The second parameter is <math> p_1 </math> which is the current pressure reading. In order to generate the relative change in height <math> m_\Delta</math><br />
<br />
After plugging this into the formula defined above we are now left with a scalar value which represents the height displacement between the entrance and the smartphone's current location of the building [7].<br />
<br />
In order to resolve to an absolute floor level, they use the index number of the clusters of <math> m_\Delta</math> 's. As seen above <math> 5.1 </math> is the third cluster implying floor number 3.<br />
<br />
=Experiments and Results=<br />
<br />
==Dataset==<br />
<br />
In this paper, an iOS app called Sensory is developed which is used to collect data on an iPhone 6. The following sensor readings were recorded: '''indoors''', '''created at''', '''session id''', '''floor''', '''RSSI strength''', '''GPS latitude''', '''GPS longitude''', '''GPS vertical accuracy''', '''GPS horizontal accuracy''', '''GPS course''', '''GPS speed''', '''barometric relative altitude''', '''barometric pressure''', '''environment context''', '''environment mean building floors''', '''environment activity''', '''city name''', '''country name''', '''magnet x''', '''magnet y''', '''magnet z''', '''magnet total'''.<br />
<br />
As soon as the user enters or exits a building, the indoor-outdoor data has to be manually entered. To gather the data for the floor level prediction, the authors conducted 63 trials among five different buildings throughout New York City. Since unsupervised learning was being used, the actual floor level was recorded manually for the validation purposes only.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:ioaccuracy.png|450px]] </div><br />
<br />
All of these classifiers were trained and validated on data from a total of 5082 data points. The set split was 80% training and 20% validation. <br />
For the LSTM the network was trained for a total of 24 epochs with a batch size of 128 and using an Adam optimizer where the learning rate was 0.006. <br />
Although the baselines performed considerably well the objective here was to show that an LSTM can be used in the future to model the entire system with an LSTM.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:flooraccuracy.png|650px]] </div><br />
<br />
The above chart shows the success that their system is able to achieve in the floor level prediction.<br />
<br />
The performance was measured in terms of how many floors were travelled rather than the absolute floor number. Because different buildings might have their floors differently numbered. They used different m values in 2 tests. One applies the same m value across all building and the other one applied specific m values on different buildings. The result showed that this specification on m values hugely increased the accuracy.<br />
<br />
=Future Work=<br />
The first part of the system used an LSTM for indoor/outdoor classification. Therefore, this separate module can be used in many other location problems. Working on this separate problem seems to be an approach that the authors will take. They also would like to aim towards modeling the whole problem within the LSTM in order to generate the floor level predictions solely from sensor reading data.<br />
<br />
=Critique=<br />
<br />
In this paper, the authors presented a novel system which can predict a smartphone's floor level with 100% accuracy, which has not been done. Previous work relied heavily on pre-training and information regarding the building or users beforehand. Their work can generalize well to many types of tall buildings which are more than 19 stories. Another benefit to their system is that they don't need any additional infrastructure support in advance making it a practical solution for deployment. <br />
<br />
A weakness is that they claim they can get 100% accuracy, but this is only if they know the floor to ceiling height, and their accuracy relies on this key piece of information. Otherwise, when conditioned on the height of the building their accuracy drops by 35% to 65%. Also, the article's ideas are sometimes out of order and are repeated in cycles.<br />
<br />
It is also not clear that the LSTM is the best approach especially since a simple feedforward network achieved the same accuracy in their experiments.<br />
<br />
They also go against their claim stated at the beginning of the paper where they say they "..does not require the use of beacons, prior knowledge of the building infrastructure..." as in their clustering step they are in a way using prior knowledge from previous visits [4].<br />
<br />
The authors also recognize several potential failings of their method. One is that their algorithm will not differentiate based on the floor of the building the user entered on (if there are entrances on multiple floors). In addition, they state that a user on the roof could be detected as being on the ground floor. It was not mentioned/explored in the paper, but a person being on a balcony (ex: attached to an apartment) may have the same effect. These sources of error will need to be corrected before this or a similar algorithm is implemented; otherwise, the algorithm may provide the misleading data to rescue crews, etc.<br />
<br />
Overall this paper is not too novel, as they don't provide any algorithmic improvement over the state of the art. Their methods are fairly standard ML techniques and they have only used out of the box solutions. There is no clear intuition why the proposed work well for the authors. This application could be solved using simpler methods like having an emergency push button on each floor. Moreover, authors don't provide sufficient motivation for why deep learning would be a good solution to this problem.<br />
<br />
The proposed model could introduce privacy risks such as illegal surveillance of mobile phone user and private facilities.<br />
<br />
=References=<br />
<br />
[1] Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural Computation, 9(8):<br />
1735–1780, 1997.<br />
<br />
[2] Parnandi, A., Le, K., Vaghela, P., Kolli, A., Dantu, K., Poduri, S., & Sukhatme, G. S. (2009, October). Coarse in-building localization with smartphones. In International Conference on Mobile Computing, Applications, and Services (pp. 343-354). Springer, Berlin, Heidelberg.<br />
<br />
[3] Wonsang Song, Jae Woo Lee, Byung Suk Lee, Henning Schulzrinne. "Finding 9-1-1 Callers in Tall Buildings". IEEE WoWMoM '14. Sydney, Australia, June 2014.<br />
<br />
[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and Smartphone Sensor Data, 2018<br />
<br />
[5] Kawakubo, Hideko and Hiroaki Yoshida. “Rapid Feature Selection Based on Random Forests for High-Dimensional Data.” (2012).<br />
<br />
[6] James Bergstra and Yoshua Bengio. 2012. Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13 (February 2012), 281-305.<br />
<br />
[7] Greg Milette, Adam Stroud: Professional Android Sensor Programming, 2012, Wiley India</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data&diff=42233Predicting Floor Level For 911 Calls with Neural Network and Smartphone Sensor Data2018-12-03T03:44:01Z<p>A22ravi: /* Introduction */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
In highly populated cities with many buildings, locating individuals in the case of an emergency is an important task. For emergency responders, time is of essence. Therefore, accurately locating a 911 caller plays an integral role in this important process.<br />
<br />
The motivation for this problem is in the context of 911 calls: victims trapped in a tall building who seek immediate medical attention, locating emergency personnel such as firefighters or paramedics, or a minor calling on behalf of an incapacitated adult. <br />
<br />
In this paper, a novel approach is presented to accurately predict floor level for 911 calls by leveraging neural networks and sensor data from smartphones.<br />
<br />
In large cities with tall buildings, relying on GPS or Wi-Fi signals does not always lead to an accurate location of a caller.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:17floor.png|250px]]<br />
[[File:19floor.png|250px]]</div><br />
<br />
<br />
In this work, there are two major contributions. The first is that they trained a LSTM to classify whether a smartphone was either inside or outside a building using GPS, Received signal strength indication (RSSI), and magnetometer sensor readings. The model is compared with baseline models like feed-forward neural networks, logistic regression, SVM, HMM, and Random Forests. The second contribution is an algorithm, which uses the output of the trained LSTM, to predict change in the barometric pressure of the smartphone from when it first entered the building against that of its current location within the building. In the final part of their algorithm, they are able to predict the floor level by clustering the measurements of height.<br />
<br />
The model does not rely on the external sensors placed inside the building, prior knowledge of the building, nor user movement behaviour. The only input it looks at is the GPS and the barometric signal from the phone. Finally, they also talk about the application of this algorithm in a variety of other real-world situations. <br />
<br />
All the codes and data related to this article are available here[[https://github.com/williamFalcon/Predicting-floor-level-for-911-Calls-with-Neural-Networks-and-Smartphone-Sensor-Data]]<br />
<br />
=Related Work=<br />
<br />
<br />
In general, previous work falls under two categories. The first category of methods is the classification methods based on the user's activity. <br />
Therefore, some current methods leverage the user's activity to predict which is based on the offset in their movement [2]. These activities include running, walking, and moving through the elevator.<br />
The second set of methods focus more on the use of a barometer which measures the atmospheric pressure. As a result, utilizing a barometer can provide the changes in altitude.<br />
<br />
Avinash Parnandi and his coauthors used multiple classifiers in the predicting the floor level [2]. The steps in their algorithmic process are: <br />
<ol><br />
<li> Classifier to predict whether the user is indoors or outdoors</li><br />
<li> Classifier to identify if the activity of the user, i.e. walking, standing still etc. </li><br />
<li> Classifier to measure the displacement</li><br />
</ol><br />
<br />
One of the downsides of this work is to achieve the high accuracy that the user's step size is needed, therefore heavily relying on pre-training to the specific users. In a real world application of this method, this would not be practical.<br />
<br />
<br />
Song and his colleagues model the way or cause of ascent. That is, was the ascent a result of taking the elevator, stairs or escalator [3]. Then by using infrastructure support of the buildings and as well as additional tuning they are able to predict floor level. <br />
This method also suffers from relying on data specific to the building. <br />
<br />
Overall, these methods suffer from relying on pre-training to a specific user, needing additional infrastructure support, or data specific to the building. The method proposed in this paper aims to predict floor level without these constraints.<br />
<br />
=Method=<br />
<br />
<br />
In their paper, the authors claim that to their knowledge "there does not exist a dataset for predicting floor heights" [4].<br />
<br />
To collect data, the authors developed an iOS application (called Sensory) that runs on an iPhone 6s to aggregate the data. They used the smartphone's sensors to record different features such as barometric pressure, GPS course, GPS speed, RSSI strength, GPS longitude, GPS latitude, and altitude. The app streamed data at 1 sample per second, and each datum contained the different sensor measurements mentions earlier along with environment contexts like building floors, environment activity, city name, country name, and magnetic strength.<br />
<br />
The data collection procedure for indoor-outdoor classifier was described as follows:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) As soon as we exit, set indoors to 0. 7) Stop recording. 8) Save data as CSV for analysis. This procedure can start either outside or inside a building without loss of generality.<br />
<br />
The following procedure generates data used to predict a floor change from the entrance floor to the end floor:<br />
1) Start outside a building. 2) Turn Sensor on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) Finally, enter a building and ascend/descend to any story. 7) Ascend through any method desired, stairs, elevator, escalator, etc. 8) Once at the floor, stop recording. 9) Save data as CSV for analysis.<br />
<br />
Their algorithm was used to predict floor level which is a 3 part process:<br />
<br />
<ol><br />
<li> Classifying whether smartphone is indoor or outdoor </li><br />
<li> Indoor/Outdoor Transition detector</li><br />
<li> Estimating vertical height and resolving to absolute floor level </li><br />
</ol><br />
<br />
==1) Classifying Indoor/Outdoor ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:classifierfloor.png|800px]] </div><br />
<br />
From [5] they are using 6 features which were found through forests of trees feature reduction. The features are smartphone's barometric pressure (<math>P</math>), GPS vertical accuracy (<math>GV</math>), GPS horizontal accuracy (<math>GH</math>), GPS speed (<math>S</math>), device RSSI level (<math>rssi</math>), and magnetometer total reading (<math>M</math>).<br />
<br />
The magnetometer total reading was calculated from given the 3-dimensional reading <math>x, y, z </math><br />
<br />
<br />
<div style="text-align: center;">Total Magnetic field strength <math>= M = \sqrt{x^{2} + y^{2} + z^{2}}</math></div><br />
<br />
They used a 3 layer LSTM where the inputs are <math> d </math> consecutive time steps. The output <math> y = 1 </math> if smartphone is indoor and <math> y = 0 </math> if smartphone is outdoor.<br />
<br />
In their design they set <math> d = 3</math> by random search [6]. The point to make is that they wanted the network to learn the relationship given a little bit of information from both the past and future.<br />
<br />
For the overall signal sequence: <math> \{x_1, x_2,x_j, ... , x_n\}</math> the aim is to classify <math> d </math> consecutive sensor readings <math> X_i = \{x_1, x_2, ..., x_d \} </math> as <math> y = 1 </math> or <math> y = 0 </math> as noted above.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Table5.png|750px]] </div><br />
<br />
This is a critical part of their system and they only focus on the predictions in the subspace of being indoors. <br />
<br />
They have trained the LSTM to minimize the binary cross entropy between the true indoor state <math> y </math> of example <math> i </math>. <br />
<br />
The cost function is shown below:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:costfunction.png|450px]] </div><br />
<br />
The final output of the LSTM is a time-series <math> T = {t_1, t_2, ..., t_i, t_n} </math> where each <math> t_i = 0, t_i = 1 </math> if the point is outside or inside respectively.<br />
<br />
==2) Transition Detector ==<br />
<br />
Given the predictions from the previous step, now the next part is to find when the transition of going in or out of a building has occurred.<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:transition.png|400px]] </div><br />
In this figure, they convolve filters <math> V_1, V_2</math> across the predictions T and they pick a subset <math>s_i </math> such that the Jacard distance (defined below) is <math> >= 0.4 </math><br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:v1v2.png|250px]] </div><br />
Jacard Distance:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:jacard.png|450px]]</div><br />
<br />
After this process, we are now left with a set of <math> b_i</math>'s describing the index of each indoor/outdoor transition. The process is shown in the first figure.<br />
<br />
==3) Vertical height and floor level ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:resolvefloor.png|700px]] </div><br />
<br />
[3] suggested the use of a reference barometer or beacons as a way to determine the entrances to a building.<br />
<br />
However, such need is eliminated by the authors' approach. The authors' second key contribution is to use the LSTM IO predictions to help identifying these indoor transitions into the building. The LSTM provides a self-contained estimator of a building’s entrance without relying on external sensor information on a user’s body or beacons placed inside a building’s lobby. [4]<br />
<br />
In the final part of the system, the vertical offset needs to be computed given the smartphone's last known location i.e. the last known transition which can easily be computed given the set of transitions from the previous step. All that needs to be done is to pull the index of most recent transition from the previous step and set <math> p_0</math> to the lowest pressure within a ~ 15-second window around that index.<br />
<br />
The second parameter is <math> p_1 </math> which is the current pressure reading. In order to generate the relative change in height <math> m_\Delta</math><br />
<br />
After plugging this into the formula defined above we are now left with a scalar value which represents the height displacement between the entrance and the smartphone's current location of the building [7].<br />
<br />
In order to resolve to an absolute floor level, they use the index number of the clusters of <math> m_\Delta</math> 's. As seen above <math> 5.1 </math> is the third cluster implying floor number 3.<br />
<br />
=Experiments and Results=<br />
<br />
==Dataset==<br />
<br />
In this paper, an iOS app called Sensory is developed which is used to collect data on an iPhone 6. The following sensor readings were recorded: '''indoors''', '''created at''', '''session id''', '''floor''', '''RSSI strength''', '''GPS latitude''', '''GPS longitude''', '''GPS vertical accuracy''', '''GPS horizontal accuracy''', '''GPS course''', '''GPS speed''', '''barometric relative altitude''', '''barometric pressure''', '''environment context''', '''environment mean building floors''', '''environment activity''', '''city name''', '''country name''', '''magnet x''', '''magnet y''', '''magnet z''', '''magnet total'''.<br />
<br />
As soon as the user enters or exits a building, the indoor-outdoor data has to be manually entered. To gather the data for the floor level prediction, the authors conducted 63 trials among five different buildings throughout New York City. Since unsupervised learning was being used, the actual floor level was recorded manually for the validation purposes only.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:ioaccuracy.png|450px]] </div><br />
<br />
All of these classifiers were trained and validated on data from a total of 5082 data points. The set split was 80% training and 20% validation. <br />
For the LSTM the network was trained for a total of 24 epochs with a batch size of 128 and using an Adam optimizer where the learning rate was 0.006. <br />
Although the baselines performed considerably well the objective here was to show that an LSTM can be used in the future to model the entire system with an LSTM.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:flooraccuracy.png|650px]] </div><br />
<br />
The above chart shows the success that their system is able to achieve in the floor level prediction.<br />
<br />
The performance was measured in terms of how many floors were travelled rather than the absolute floor number. Because different buildings might have their floors differently numbered. They used different m values in 2 tests. One applies the same m value across all building and the other one applied specific m values on different buildings. The result showed that this specification on m values hugely increased the accuracy.<br />
<br />
=Future Work=<br />
The first part of the system used an LSTM for indoor/outdoor classification. Therefore, this separate module can be used in many other location problems. Working on this separate problem seems to be an approach that the authors will take. They also would like to aim towards modeling the whole problem within the LSTM in order to generate the floor level predictions solely from sensor reading data.<br />
<br />
=Critique=<br />
<br />
In this paper, the authors presented a novel system which can predict a smartphone's floor level with 100% accuracy, which has not been done. Previous work relied heavily on pre-training and information regarding the building or users beforehand. Their work can generalize well to many types of tall buildings which are more than 19 stories. Another benefit to their system is that they don't need any additional infrastructure support in advance making it a practical solution for deployment. <br />
<br />
A weakness is that they claim they can get 100% accuracy, but this is only if they know the floor to ceiling height, and their accuracy relies on this key piece of information. Otherwise, when conditioned on the height of the building their accuracy drops by 35% to 65%. Also, the article's ideas are sometimes out of order and are repeated in cycles.<br />
<br />
It is also not clear that the LSTM is the best approach especially since a simple feedforward network achieved the same accuracy in their experiments.<br />
<br />
They also go against their claim stated at the beginning of the paper where they say they "..does not require the use of beacons, prior knowledge of the building infrastructure..." as in their clustering step they are in a way using prior knowledge from previous visits [4].<br />
<br />
The authors also recognize several potential failings of their method. One is that their algorithm will not differentiate based on the floor of the building the user entered on (if there are entrances on multiple floors). In addition, they state that a user on the roof could be detected as being on the ground floor. It was not mentioned/explored in the paper, but a person being on a balcony (ex: attached to an apartment) may have the same effect. These sources of error will need to be corrected before this or a similar algorithm is implemented; otherwise, the algorithm may provide the misleading data to rescue crews, etc.<br />
<br />
Overall this paper is not too novel, as they don't provide any algorithmic improvement over the state of the art. Their methods are fairly standard ML techniques and they have only used out of the box solutions. There is no clear intuition why the proposed work well for the authors. This application could be solved using simpler methods like having an emergency push button on each floor. Moreover, authors don't provide sufficient motivation for why deep learning would be a good solution to this problem.<br />
<br />
The proposed model could introduce privacy risks such as illegal surveillance of mobile phone user and private facilities.<br />
<br />
=References=<br />
<br />
[1] Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural Computation, 9(8):<br />
1735–1780, 1997.<br />
<br />
[2] Parnandi, A., Le, K., Vaghela, P., Kolli, A., Dantu, K., Poduri, S., & Sukhatme, G. S. (2009, October). Coarse in-building localization with smartphones. In International Conference on Mobile Computing, Applications, and Services (pp. 343-354). Springer, Berlin, Heidelberg.<br />
<br />
[3] Wonsang Song, Jae Woo Lee, Byung Suk Lee, Henning Schulzrinne. "Finding 9-1-1 Callers in Tall Buildings". IEEE WoWMoM '14. Sydney, Australia, June 2014.<br />
<br />
[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and Smartphone Sensor Data, 2018<br />
<br />
[5] Kawakubo, Hideko and Hiroaki Yoshida. “Rapid Feature Selection Based on Random Forests for High-Dimensional Data.” (2012).<br />
<br />
[6] James Bergstra and Yoshua Bengio. 2012. Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13 (February 2012), 281-305.<br />
<br />
[7] Greg Milette, Adam Stroud: Professional Android Sensor Programming, 2012, Wiley India</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data&diff=42232Predicting Floor Level For 911 Calls with Neural Network and Smartphone Sensor Data2018-12-03T03:42:26Z<p>A22ravi: /* Method */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
In highly populated cities with many buildings, locating individuals in the case of an emergency is an important task. For emergency responders, time is of essence. Therefore, accurately locating a 911 caller plays an integral role in this important process.<br />
<br />
The motivation for this problem is in the context of 911 calls: victims trapped in a tall building who seek immediate medical attention, locating emergency personnel such as firefighters or paramedics, or a minor calling on behalf of an incapacitated adult. <br />
<br />
In this paper, a novel approach is presented to accurately predict floor level for 911 calls by leveraging neural networks and sensor data from smartphones.<br />
<br />
In large cities with tall buildings, relying on GPS or Wi-Fi signals does not always lead to an accurate location of a caller.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:17floor.png|250px]]<br />
[[File:19floor.png|250px]]</div><br />
<br />
<br />
In this work, there are two major contributions. The first is that they trained a LSTM to classify whether a smartphone was either inside or outside a building using GPS, RSSI, and magnetometer sensor readings. The model is compared with baseline models like feed-forward neural networks, logistic regression, SVM, HMM, and Random Forests. The second contribution is an algorithm, which uses the output of the trained LSTM, to predict change in the barometric pressure of the smartphone from when it first entered the building against that of its current location within the building. In the final part of their algorithm, they are able to predict the floor level by clustering the measurements of height.<br />
<br />
The model does not rely on the external sensors placed inside the building, prior knowledge of the building, nor user movement behaviour. The only input it looks at is the GPS and the barometric signal from the phone. Finally, they also talk about the application of this algorithm in a variety of other real-world situations. <br />
<br />
All the codes and data related to this article are available here[[https://github.com/williamFalcon/Predicting-floor-level-for-911-Calls-with-Neural-Networks-and-Smartphone-Sensor-Data]]<br />
<br />
=Related Work=<br />
<br />
<br />
In general, previous work falls under two categories. The first category of methods is the classification methods based on the user's activity. <br />
Therefore, some current methods leverage the user's activity to predict which is based on the offset in their movement [2]. These activities include running, walking, and moving through the elevator.<br />
The second set of methods focus more on the use of a barometer which measures the atmospheric pressure. As a result, utilizing a barometer can provide the changes in altitude.<br />
<br />
Avinash Parnandi and his coauthors used multiple classifiers in the predicting the floor level [2]. The steps in their algorithmic process are: <br />
<ol><br />
<li> Classifier to predict whether the user is indoors or outdoors</li><br />
<li> Classifier to identify if the activity of the user, i.e. walking, standing still etc. </li><br />
<li> Classifier to measure the displacement</li><br />
</ol><br />
<br />
One of the downsides of this work is to achieve the high accuracy that the user's step size is needed, therefore heavily relying on pre-training to the specific users. In a real world application of this method, this would not be practical.<br />
<br />
<br />
Song and his colleagues model the way or cause of ascent. That is, was the ascent a result of taking the elevator, stairs or escalator [3]. Then by using infrastructure support of the buildings and as well as additional tuning they are able to predict floor level. <br />
This method also suffers from relying on data specific to the building. <br />
<br />
Overall, these methods suffer from relying on pre-training to a specific user, needing additional infrastructure support, or data specific to the building. The method proposed in this paper aims to predict floor level without these constraints.<br />
<br />
=Method=<br />
<br />
<br />
In their paper, the authors claim that to their knowledge "there does not exist a dataset for predicting floor heights" [4].<br />
<br />
To collect data, the authors developed an iOS application (called Sensory) that runs on an iPhone 6s to aggregate the data. They used the smartphone's sensors to record different features such as barometric pressure, GPS course, GPS speed, RSSI strength, GPS longitude, GPS latitude, and altitude. The app streamed data at 1 sample per second, and each datum contained the different sensor measurements mentions earlier along with environment contexts like building floors, environment activity, city name, country name, and magnetic strength.<br />
<br />
The data collection procedure for indoor-outdoor classifier was described as follows:<br />
1) Start outside a building. 2) Turn Sensory on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) As soon as we exit, set indoors to 0. 7) Stop recording. 8) Save data as CSV for analysis. This procedure can start either outside or inside a building without loss of generality.<br />
<br />
The following procedure generates data used to predict a floor change from the entrance floor to the end floor:<br />
1) Start outside a building. 2) Turn Sensor on, set indoors to 0. 3) Start recording. 4) Walk into and out of buildings over the next n seconds. 5) As soon as we enter the building (cross the outermost door) set indoors to 1. 6) Finally, enter a building and ascend/descend to any story. 7) Ascend through any method desired, stairs, elevator, escalator, etc. 8) Once at the floor, stop recording. 9) Save data as CSV for analysis.<br />
<br />
Their algorithm was used to predict floor level which is a 3 part process:<br />
<br />
<ol><br />
<li> Classifying whether smartphone is indoor or outdoor </li><br />
<li> Indoor/Outdoor Transition detector</li><br />
<li> Estimating vertical height and resolving to absolute floor level </li><br />
</ol><br />
<br />
==1) Classifying Indoor/Outdoor ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:classifierfloor.png|800px]] </div><br />
<br />
From [5] they are using 6 features which were found through forests of trees feature reduction. The features are smartphone's barometric pressure (<math>P</math>), GPS vertical accuracy (<math>GV</math>), GPS horizontal accuracy (<math>GH</math>), GPS speed (<math>S</math>), device RSSI level (<math>rssi</math>), and magnetometer total reading (<math>M</math>).<br />
<br />
The magnetometer total reading was calculated from given the 3-dimensional reading <math>x, y, z </math><br />
<br />
<br />
<div style="text-align: center;">Total Magnetic field strength <math>= M = \sqrt{x^{2} + y^{2} + z^{2}}</math></div><br />
<br />
They used a 3 layer LSTM where the inputs are <math> d </math> consecutive time steps. The output <math> y = 1 </math> if smartphone is indoor and <math> y = 0 </math> if smartphone is outdoor.<br />
<br />
In their design they set <math> d = 3</math> by random search [6]. The point to make is that they wanted the network to learn the relationship given a little bit of information from both the past and future.<br />
<br />
For the overall signal sequence: <math> \{x_1, x_2,x_j, ... , x_n\}</math> the aim is to classify <math> d </math> consecutive sensor readings <math> X_i = \{x_1, x_2, ..., x_d \} </math> as <math> y = 1 </math> or <math> y = 0 </math> as noted above.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Table5.png|750px]] </div><br />
<br />
This is a critical part of their system and they only focus on the predictions in the subspace of being indoors. <br />
<br />
They have trained the LSTM to minimize the binary cross entropy between the true indoor state <math> y </math> of example <math> i </math>. <br />
<br />
The cost function is shown below:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:costfunction.png|450px]] </div><br />
<br />
The final output of the LSTM is a time-series <math> T = {t_1, t_2, ..., t_i, t_n} </math> where each <math> t_i = 0, t_i = 1 </math> if the point is outside or inside respectively.<br />
<br />
==2) Transition Detector ==<br />
<br />
Given the predictions from the previous step, now the next part is to find when the transition of going in or out of a building has occurred.<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:transition.png|400px]] </div><br />
In this figure, they convolve filters <math> V_1, V_2</math> across the predictions T and they pick a subset <math>s_i </math> such that the Jacard distance (defined below) is <math> >= 0.4 </math><br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:v1v2.png|250px]] </div><br />
Jacard Distance:<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:jacard.png|450px]]</div><br />
<br />
After this process, we are now left with a set of <math> b_i</math>'s describing the index of each indoor/outdoor transition. The process is shown in the first figure.<br />
<br />
==3) Vertical height and floor level ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:resolvefloor.png|700px]] </div><br />
<br />
[3] suggested the use of a reference barometer or beacons as a way to determine the entrances to a building.<br />
<br />
However, such need is eliminated by the authors' approach. The authors' second key contribution is to use the LSTM IO predictions to help identifying these indoor transitions into the building. The LSTM provides a self-contained estimator of a building’s entrance without relying on external sensor information on a user’s body or beacons placed inside a building’s lobby. [4]<br />
<br />
In the final part of the system, the vertical offset needs to be computed given the smartphone's last known location i.e. the last known transition which can easily be computed given the set of transitions from the previous step. All that needs to be done is to pull the index of most recent transition from the previous step and set <math> p_0</math> to the lowest pressure within a ~ 15-second window around that index.<br />
<br />
The second parameter is <math> p_1 </math> which is the current pressure reading. In order to generate the relative change in height <math> m_\Delta</math><br />
<br />
After plugging this into the formula defined above we are now left with a scalar value which represents the height displacement between the entrance and the smartphone's current location of the building [7].<br />
<br />
In order to resolve to an absolute floor level, they use the index number of the clusters of <math> m_\Delta</math> 's. As seen above <math> 5.1 </math> is the third cluster implying floor number 3.<br />
<br />
=Experiments and Results=<br />
<br />
==Dataset==<br />
<br />
In this paper, an iOS app called Sensory is developed which is used to collect data on an iPhone 6. The following sensor readings were recorded: '''indoors''', '''created at''', '''session id''', '''floor''', '''RSSI strength''', '''GPS latitude''', '''GPS longitude''', '''GPS vertical accuracy''', '''GPS horizontal accuracy''', '''GPS course''', '''GPS speed''', '''barometric relative altitude''', '''barometric pressure''', '''environment context''', '''environment mean building floors''', '''environment activity''', '''city name''', '''country name''', '''magnet x''', '''magnet y''', '''magnet z''', '''magnet total'''.<br />
<br />
As soon as the user enters or exits a building, the indoor-outdoor data has to be manually entered. To gather the data for the floor level prediction, the authors conducted 63 trials among five different buildings throughout New York City. Since unsupervised learning was being used, the actual floor level was recorded manually for the validation purposes only.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:ioaccuracy.png|450px]] </div><br />
<br />
All of these classifiers were trained and validated on data from a total of 5082 data points. The set split was 80% training and 20% validation. <br />
For the LSTM the network was trained for a total of 24 epochs with a batch size of 128 and using an Adam optimizer where the learning rate was 0.006. <br />
Although the baselines performed considerably well the objective here was to show that an LSTM can be used in the future to model the entire system with an LSTM.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:flooraccuracy.png|650px]] </div><br />
<br />
The above chart shows the success that their system is able to achieve in the floor level prediction.<br />
<br />
The performance was measured in terms of how many floors were travelled rather than the absolute floor number. Because different buildings might have their floors differently numbered. They used different m values in 2 tests. One applies the same m value across all building and the other one applied specific m values on different buildings. The result showed that this specification on m values hugely increased the accuracy.<br />
<br />
=Future Work=<br />
The first part of the system used an LSTM for indoor/outdoor classification. Therefore, this separate module can be used in many other location problems. Working on this separate problem seems to be an approach that the authors will take. They also would like to aim towards modeling the whole problem within the LSTM in order to generate the floor level predictions solely from sensor reading data.<br />
<br />
=Critique=<br />
<br />
In this paper, the authors presented a novel system which can predict a smartphone's floor level with 100% accuracy, which has not been done. Previous work relied heavily on pre-training and information regarding the building or users beforehand. Their work can generalize well to many types of tall buildings which are more than 19 stories. Another benefit to their system is that they don't need any additional infrastructure support in advance making it a practical solution for deployment. <br />
<br />
A weakness is that they claim they can get 100% accuracy, but this is only if they know the floor to ceiling height, and their accuracy relies on this key piece of information. Otherwise, when conditioned on the height of the building their accuracy drops by 35% to 65%. Also, the article's ideas are sometimes out of order and are repeated in cycles.<br />
<br />
It is also not clear that the LSTM is the best approach especially since a simple feedforward network achieved the same accuracy in their experiments.<br />
<br />
They also go against their claim stated at the beginning of the paper where they say they "..does not require the use of beacons, prior knowledge of the building infrastructure..." as in their clustering step they are in a way using prior knowledge from previous visits [4].<br />
<br />
The authors also recognize several potential failings of their method. One is that their algorithm will not differentiate based on the floor of the building the user entered on (if there are entrances on multiple floors). In addition, they state that a user on the roof could be detected as being on the ground floor. It was not mentioned/explored in the paper, but a person being on a balcony (ex: attached to an apartment) may have the same effect. These sources of error will need to be corrected before this or a similar algorithm is implemented; otherwise, the algorithm may provide the misleading data to rescue crews, etc.<br />
<br />
Overall this paper is not too novel, as they don't provide any algorithmic improvement over the state of the art. Their methods are fairly standard ML techniques and they have only used out of the box solutions. There is no clear intuition why the proposed work well for the authors. This application could be solved using simpler methods like having an emergency push button on each floor. Moreover, authors don't provide sufficient motivation for why deep learning would be a good solution to this problem.<br />
<br />
The proposed model could introduce privacy risks such as illegal surveillance of mobile phone user and private facilities.<br />
<br />
=References=<br />
<br />
[1] Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. Neural Computation, 9(8):<br />
1735–1780, 1997.<br />
<br />
[2] Parnandi, A., Le, K., Vaghela, P., Kolli, A., Dantu, K., Poduri, S., & Sukhatme, G. S. (2009, October). Coarse in-building localization with smartphones. In International Conference on Mobile Computing, Applications, and Services (pp. 343-354). Springer, Berlin, Heidelberg.<br />
<br />
[3] Wonsang Song, Jae Woo Lee, Byung Suk Lee, Henning Schulzrinne. "Finding 9-1-1 Callers in Tall Buildings". IEEE WoWMoM '14. Sydney, Australia, June 2014.<br />
<br />
[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and Smartphone Sensor Data, 2018<br />
<br />
[5] Kawakubo, Hideko and Hiroaki Yoshida. “Rapid Feature Selection Based on Random Forests for High-Dimensional Data.” (2012).<br />
<br />
[6] James Bergstra and Yoshua Bengio. 2012. Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13 (February 2012), 281-305.<br />
<br />
[7] Greg Milette, Adam Stroud: Professional Android Sensor Programming, 2012, Wiley India</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946w18/Towards_Image_Understanding_From_Deep_Compression_Without_Decoding&diff=42220stat946w18/Towards Image Understanding From Deep Compression Without Decoding2018-12-02T23:37:06Z<p>A22ravi: Undo revision 42128 by R82zhang (talk)</p>
<hr />
<div>Paper Title: Towards Image Understanding from Deep Compression Without Decoding - ICLR 2018<br />
<br />
Presented By: Aravind Ravi<br />
<br />
== Introduction ==<br />
Recent advances in the deep neural network (DNN) based image compression methods have shown potential improvements in image quality, savings in storage and bandwidth reduction. These methods leverage common neural network architectures such as convolutional autoencoders or recurrent neural networks to compress and reconstruct RGB images and outperform classical techniques such as JPEG2000 and BPG on perceptual metrics such as structural similarity index (SSIM) and multi-scale structural similarity index (MS-SSIM).<br />
<br />
These approaches encode an image <math>x </math> to some feature map (compressed representation), which is subsequently quantized to a set of symbols <math>z </math>. These symbols are then losslessly compressed to a bitstream, from which a decoder reconstructs an image <math>{\hat{x}} </math>, of the same dimensions as <math>x </math>.<br />
<br />
Learned compression algorithms have an advantage over engineering compression algorithms in that they can be much more easily adapted to specific domains. For example, a learned compression algorithm might be able to learn good performance on compressing medical images, without specifically tuning the algorithm.<br />
<br />
In this paper, the authors explore the idea of applying the learned representations to perform inference without reconstructing the compressed image. Specifically, instead of reconstructing an RGB image from the compressed representation and feeding it to a network for inference, the paper proposes to use a modified network that bypasses reconstruction of the RGB image.<br />
<br />
The rationale behind this approach is that the neural network architectures commonly used for learned compression (in particular the encoders) are similar to the ones commonly used for inference, and learned image encoders are hence, in principle, capable of extracting features relevant for inference tasks. The encoder might learn features relevant for inference purely by training on the compression task, and can be forced to learn these features by training on the compression and inference tasks jointly.<br />
<br />
The advantage of learning an encoder for image compression which produces compressed representation containing features relevant for inference is obvious in scenarios where images are transmitted (e.g. from a mobile device) before processing (e.g. in the cloud), as it saves reconstruction of the RGB image as well as part of the feature extraction and hence speeds up processing. A typical use case is a cloud photo storage application where every image is processed immediately upon upload for indexing and search purposes.<br />
<br />
Note: [https://en.wikipedia.org/wiki/Structural_similarity More Information on SSIM, MSSIM]<br />
<br />
== Intuition ==<br />
<br />
Compression techniques (something as common as zipping) are commonly used by us in day to day file handling tasks. Most often we use engineered compression techniques. Deep Neural Networks (DNNs) are nonlinear function approximators which act as feature extractors, extracting features from inputs (like images or sound files). These can be seen as learning based compression techniques as they can perform compression and they can be trained using back propagation as well. If image classification can be done on these compressed files, large image data sets like hyperspectral images and MRI images can be stored efficiently and the compressed files can be used directly by the DNNs for classification or reinforcement learning tasks.<br />
<br />
==Motivation and Contributions==<br />
The authors propose to perform image understanding tasks such as image classification and segmentation directly on DNN based compressed representations. Performing the image understanding tasks on the compressed representations/encoded feature maps has two advantages. <br />
# This method bypasses the process of decoding the image into the RGB space before classification.<br />
# The authors show that it reduces the overall computational complexity up to 2 times.<br />
<br />
=== Contributions of the Paper ===<br />
* A method to perform image classification and semantic segmentation from compressed representations. In large scale image understanding problems, learning from a compressed representation is definitely something that is interesting. <br />
* The proposed method offers classification accuracy similar to that achieved on decompressed images while reducing the computational complexity by 2 times.<br />
* Semantic segmentation has been shown to be as accurate as performance on decompressed images for moderate compression rates and higher accuracy for aggressive compression rates. In addition, this method achieves lower computational complexity.<br />
* Joint training for image compression and classification has been shown to improve the quality of the image and increase in accuracy of classification and segmentation.<br />
<br />
==Related Work==<br />
<br />
The prior work has shown image classification from compressed images based on engineered codecs. Some of the works in this area are:<br />
<br />
* In video analysis domain: Action recognition (Yeo et al., 2008; Kantorov & Laptev, 2014)<br />
* Classification of compressed hyperspectral images (Hahn et al., 2014; Aghagolzadeh & Radha, 2015)<br />
* Discrete Cosine Transform based compression performed on images before feeding into a neural network, which shows an improvement in training speed by up to 10 times Fu & Guimaraes (2016)<br />
* Video analysis on compressed video (using engineered codecs) has also been studied in the past (Babu et al., 2016)<br />
* Criticism on document image analysis methods (Javed et al.2017)<br />
<br />
The authors propose a method that does inference on top of learned feature representation and hence has a direct relation to unsupervised feature learning using autoencoders.<br />
They also claim that so far there hasn't been any work using learned compressed representations for image classification and segmentation.<br />
<br />
==Learned Deeply Compressed Representations==<br />
<br />
The image compression task is performed based on a convolutional autoencoder architecture proposed by Theis et al. 2017 (shown in the figure below), and a variant of the training procedure described by Agustsson et. al 2017. <br />
<br />
[[File:AR_theisAutoencoder.png|600px|center]]<br />
<br />
Some points to better understand the architecture:<br />
<br />
1. Most convolutions are done in a convolved, lower-dimensional space to speed up computation<br />
<br />
2. Different activation functions are used. Blank arrows indicate the identity function (no additional linearity), while black arrows indicate leaky rectifications<br />
<br />
3. The “round” box simply rounds all elements in the tensor to the nearest integer<br />
<br />
4. The “subpix” block is just an upsampling /reconstruction block where the feature map’s coefficients are reshuffled after a convolution<br />
<br />
<br />
<br />
=== Compression Architecture ===<br />
<br />
The compression network is an autoencoder that takes an input image <math>x </math> and outputs <math>{\hat{x}} </math> as the approximation to the input. <br />
<br />
[[File:AR_Fig2a.png|300px|center]]<br />
<br />
The encoder has the following structure: It starts with 2 convolutional layers with spatial subsampling by a factor of 2, followed by 3 residual units, and a final convolutional layer with spatial subsampling by a factor of 2. This results in a <math>w/8</math> x <math>h/8</math> x <math>C</math> dimensional representation, where <math>w </math> and <math>h </math> are the spatial dimensions of <math>x </math>, and the number of channels C is a hyperparameter related to the rate <math>R </math>. This representation is then quantized to a discrete set of symbols, forming a compressed representation, <math>z </math>.<br />
<br />
To get the reconstruction <math>{\hat{x}} </math>, the compressed representation is fed into the decoder, which mirrors the encoder, but uses upsampling and deconvolutions instead of subsampling and convolutions.<br />
<br />
Quantizing the compressed representation imposes a distortion <math>D </math> on <math>{\hat{x}} </math> w.r.t. <math>x </math>, i.e., it increases the reconstruction error. This is traded for a decrease in entropy of the quantized compressed representation<br />
<math>z </math> which leads to a decrease of the length of the bitstream as measured by the rate <math>R </math>. Thus, to train the image compression network, the classical rate-distortion trade-off <math>D + \beta R</math> is minimized. As a metric for <math>D </math>, the mean squared error (MSE) between <math>x </math> and <math>{\hat{x}} </math> are used and <math>R</math> is estimated using<br />
<math>H(q)</math>. <math>H(q)</math> is the entropy of the probability distribution over the symbols and is estimated using a histogram of the probability distribution (as done by Agustsson et al., 2017). The trade-off between MSE and the entropy is controlled by adjusting <math>\beta </math>. For each <math>\beta </math> an operating point is derived where the images have a certain bit rate, as measured by bits per pixel (bpp), and corresponding MSE. To better control the bpp, a target entropy Ht is introduced by the authors to formulate the loss defined as:<br />
<br />
\begin{align}<br />
\mathcal{L_c} = \text{MSE}(x,{\hat{x}})+\beta\max({H(q)}-{H_t},0)<br />
\end{align}<br />
<br />
Agustsson et. al 2017, proposed a method to overcome the issue of non-differentiability of the quantization step by proposing a differentiable approximation to the quantization. This method has been adapted to suit the current application in the paper.<br />
<br />
Three operating points at 0.0983 bpp (C=8), 0.330 bpp (C=16), and 0.635 bpp (C=32) are obtained empirically. All further experiments are performed with these three operating points and the results for the same are presented in the following sections.<br />
<br />
==Image Classification from Compressed Representations==<br />
<br />
=== Classification on RGB Images ===<br />
<br />
For the image classification task based on the RGB images, the authors use the ResNet-50 architecture. <br />
Further information on residual networks can be found in the following links: <br />
[https://youtu.be/K0uoBKBQ1gA ResNets Part-1]<br />
[https://youtu.be/GSsKdtoatm8 ResNets Part-2]<br />
<br />
The details of the architecture are presented in the table below:<br />
<br />
[[File:AR_Tab1.png|400px|center]]<br />
<br />
In this paper, the number of 14x14 (conv4_x) blocks have been modified to obtain a new architecture called ResNet-71. <br />
<br />
=== Classification on Compressed Representations ===<br />
<br />
For input images with spatial dimension 224x224, the encoder of the compression network outputs a compressed representation with dimensions 28x28xC, where C is the number of channels. To use this compressed representation as input to the classification network, a simple variant of the ResNet architecture is proposed. This variant is referred to as cResNet-k, where c stands for “compressed representation” and k is the<br />
number of convolutional layers in the network. These networks are constructed by simply “cutting off” the front of the regular (RGB) ResNet. The root-block of the network and the residual layers that have a larger spatial dimension than 28x28 are removed. To adjust the number of layers k, the ResNet architecture proposed by He et al. (2015) is used and the number of 14x14 (conv4 x) residual blocks are modified.<br />
<br />
In this way, three different architectures are derived:<br />
* cResNet-39 is ResNet-50 with the first 11 layers removed as described above, and this significantly reduces computational cost<br />
* cResNet-51<br />
* cResNet-72<br />
<br />
cResNet-51 and cResNet-72 are obtained by adding 14x14 residual blocks to match the computational cost of ResNet-50 and ResNet-71 respectively.<br />
<br />
The detailed description of all the network architectures are presented below:<br />
<br />
[[File:AR_Tab3.png|600px|center]]<br />
<br />
==Semantic Segmentation from Compressed Representations==<br />
<br />
For semantic segmentation, the ResNet based DeepLab architecture is adapted for the proposed application. The cResNet<br />
and ResNet image classification architectures are re-purposed with atrous<br />
convolutions, where the filters are upsampled instead of downsampling the feature maps. This is<br />
done to increase their receptive field and to prevent aggressive subsampling of the feature maps. For segmentation, the ResNet architecture is restructured such<br />
that the output feature map has 8 times smaller spatial dimension than the original RGB image (instead<br />
subsampling by a factor 32 times like for classification). When using the cResNets the output feature<br />
map has the same spatial dimensions as the input compressed representation (instead of subsampling<br />
4 times like for classification). This results in comparably sized feature maps for both the compressed<br />
representation and the reconstructed RGB images. Finally the last 1000-way classification layer of<br />
these classification architectures is replaced by an atrous spatial pyramid pooling (ASPP) with four<br />
parallel branches with rates {6, 12, 18, 24}, which provides the final pixel-wise classification.<br />
<br />
==Joint Training for Compression and Image Classification==<br />
<br />
The authors propose a joint training strategy to combine compression and classification tasks. To do this, the proposed method combines the compression network and the cResNet-51 architecture. The figure below shows the combined pipeline:<br />
<br />
[[File:AR_Fig2b.png|300px|center]]<br />
<br />
All parts, encoder, decoder, and inference network, are trained at the same time. The compressed representation is fed<br />
to the decoder to optimize for mean-squared reconstruction error and to a cResNet-51 network to<br />
optimize for classification using a cross-entropy loss. The combined loss function takes the form:<br />
<br />
\begin{align}<br />
\mathcal{L_c} = \gamma(\text{MSE}(x,{\hat{x}})+\beta\max({H(q)}-{H_t},0))+l_{ce}(y,{\hat{y}})<br />
\end{align}<br />
<br />
where the loss terms for the compression network, <math> \mathcal{L_c} = \text{MSE}(x,{\hat{x}})+\beta\max({H(q)}-{H_t},0)</math>, are the same as in training for compression only. <math> l_{ce}</math> is the cross-entropy loss for classification.<br />
<math>\gamma </math> controls the trade-off between the compression loss and the classification loss.<br />
<br />
==Experiments and Results==<br />
<br />
=== Learned Deeply Compressed Representations Results ===<br />
<br />
All experiments have been performed on the ILSVRC2012 dataset.<br />
<br />
The metrics used to measure the compression quality are as follows: <br />
* PSNR (Peak Signal-to-Noise Ratio) is a standard measure, depending monotonically on mean squared error defined as: <br />
<br />
\begin{align}<br />
PSNR = 10(\log_{10}(255^2/MSE))<br />
\end{align}<br />
<br />
* SSIM (Structural Similarity Index) and MS-SSIM (Multi-Scale SSIM) are metrics proposed to measure the similarity of images as perceived by humans<br />
<br />
The figure below depicts the performance of the deep compression models vs. standard JPEG and JPEG2000. Higher values are better. The proposed technique outperforms the JPEG and JPEC2000 at the operating points used in this paper.<br />
<br />
[[File:AR_Fig8.png|600px|center]]<br />
<br />
The learned compressed representations are illustrated in the figure below. <br />
<br />
[[File:AR_Fig9.png|500px|center]]<br />
<br />
In the above figure, the original RGB-image is shown along with compressed versions of the RGB image which are reconstructed from the compressed representations. The 4 channels with the highest entropy are shown in the visualizations. These visualizations indicate how the networks compress an image, as the rate (bpp) gets lower the entropy cost of the network forces the<br />
compressed representation to use fewer quantization levels, as can clearly be seen. For the most aggressive compression, the channel maps use only 2 levels for the compressed representation.<br />
<br />
=== Classification on Compressed Representations ===<br />
<br />
All experiments have been performed on the ILSVRC2012 dataset. It consists of 1.28 million training images and 50k validation images. These images are distributed across 1000 diverse classes. For image classification, the top-1 classification accuracy and top-5 classification accuracy are reported on the validation set on 224x224 center crops for RGB images and 28x28 center crops for the compressed representation.<br />
<br />
==== Training Procedure ====<br />
<br />
The compression network is fixed while training the classification network, both when training with compressed representations and with reconstructed compressed RGB images. For the compressed representations, the output of the fixed encoder (the compressed representation) is provided input to the cResNets (decoder is not needed). When training on the reconstructed compressed RGB images, the output of the fixed encoder-decoder (RGB image) is provided as input to the ResNet. This is done for each operating point.<br />
<br />
Refer to Appendix A Section A4, of the paper for details on the hyperparameters and optimization used for training the network [1].<br />
<br />
==== Classification Results ====<br />
<br />
The tables below present the results of the classification at each operating point, both classifying from the compressed representation and the corresponding reconstructed compressed RGB images.<br />
<br />
[[File:AR_Tab2.png|400|center]]<br />
<br />
Figure below shows the validation curves for ResNet-50, cResNet-51, and cResNet-39. <br />
<br />
[[File:AR_Fig3.png|700|center]]<br />
<br />
For the 2 classification architectures with the same computational complexity (ResNet-50 and cResNet-51), the validation curves at the 0.635 bpp compression operating point almost coincide, with ResNet-50 performing slightly better. As the rate (bpp) gets smaller this performance gap gets smaller. The table above shows the<br />
classification results when the different architectures have converged. At the 0.635 bpp operating point, ResNet-50 only performs 0.5% better in top-5 accuracy than cResNet-51, while for the 0.0983 bpp operating point this difference is only 0.3%.<br />
Using the same pre-processing and the same learning rate schedule but starting from the original uncompressed RGB images yields 89.96% top-5 accuracy. The top-5 accuracy obtained from the compressed representation at the 0.635 bpp compression operating point, 87.85%, is even competitive<br />
with that obtained for the original images at a significantly lower storage cost. Specifically, at 0.635 bpp the ImageNet dataset requires 24.8 GB of storage space instead of 144 GB for the original version, a reduction by a factor 5.8 times.<br />
<br />
Notes on top-1 and top-5 accuracy:<br />
<br />
* Top-1 accuracy: This is the conventional accuracy metric used in machine learning. Wherein if the true label of the input to a model matches the highest probability class of the last layer of the output of CNN (predicted class probability), then the given input is correctly classified, else it is considered as incorrectly classified.<br />
* Top-5 accuracy: In this case, if any of the model's 5 highest classification probabilities match with the true label of the input, then this is considered as a correct classification, else it is an incorrect classification.<br />
<br />
===Semantic Segmentation Results===<br />
<br />
All experiments have been performed on the PASCAL VOC-2012 dataset for semantic segmentation. It has 20 object foreground classes and 1 background class. The dataset<br />
consists of 1464 training and 1449 validation images. In every image, each pixel is annotated with<br />
one of the 20 + 1 classes. The original dataset is furthermore augmented with extra annotations, so the final dataset has 10,582 images for training and 1449 images for validation.<br />
<br />
All performance is measured on pixel wise intersection-over-union (IoU) averaged over all the classes or mean-intersection-over-union (mIoU) on the validation set. <br />
<br />
[https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/ Details on IoU]<br />
<br />
==== Training Procedure ====<br />
The cResNet/ResNet networks are pre-trained on the ImageNet dataset using the procedure described earlier on the image classification task, the encoder and decoder is fixed as in the earlier scenario. The architectures are then adapted with dilated convolutions, cResNet-d/ResNet-d, and<br />
finetuned on the semantic segmentation task.<br />
<br />
Refer to Appendix A Section A5, of the paper for details on the hyperparameters and optimization used for training the network [1].<br />
<br />
==== Segmentation Results ====<br />
<br />
The table below shows the mIoU results for the segmentation task.<br />
<br />
[[File:AR_Tab2.png|450|center]]<br />
<br />
The figure below illustrates the segmentation results with respect to each compression operating point.<br />
<br />
[[File:AR_Fig4.png|700|center]]<br />
<br />
For semantic segmentation ResNet-50-d and cResNet-51-d perform equally well at the 0.635 bpp compression operating point. For the<br />
0.330 bpp operating point, segmentation from the compressed representation performs slightly better, 0.37%, and at the 0.0983 bpp operating point segmentation from the compressed representation<br />
performs considerably better than for the reconstructed compressed RGB images, by 1.65%.<br />
<br />
[[File:AR_Fig5.png|600px|center]]<br />
<br />
The above figure shows the predicted segmentation visually for both the cResNet-51-d and the ResNet-50-d<br />
architecture at each operating point. Along with the segmentation, it also shows the original uncompressed<br />
RGB image and the reconstructed compressed RGB image. These images highlight<br />
the challenging nature of these segmentation tasks, but they can nevertheless be performed using the<br />
compressed representation. They also clearly indicate that the compression affects the segmentation,<br />
as lowering the rate (bpp) progressively removes details in the image. Comparing the segmentation<br />
from the reconstructed RGB images to the segmentation from the compressed representation visually,<br />
the performance is similar.<br />
<br />
The figure below is another example of visual results of segmentation from compressed representation and reconstructed RGB<br />
images. The performance is visually similar for all operating points except for the 0.0983<br />
bpp operating point where the reconstructed RGB image fails to capture the back part of<br />
the train, while the compressed representation manages to capture that aspect of the image in the<br />
segmentation.<br />
<br />
[[File:AR_Fig10.png|600px|center]]<br />
<br />
=== Results on Computational Gains ===<br />
<br />
[[File:AR_Fig6.png|400px|center]]<br />
<br />
=====Computational Gains on Classification=====<br />
<br />
The figure on the left illustrates, the top-5 classification accuracy as a function of computational<br />
complexity for the 0.0983 bpp compression operating point.<br />
Looking at a fixed computational cost, the reconstructed compressed RGB images perform about 0.25% better. Looking at a fixed classification cost, inference from the compressed representation costs about <math>0.6 * 10^9</math> FLOPs more. However when accounting for the decoding cost at a fixed<br />
classification performance, inference from the reconstructed compressed RGB images costs <math>2.2*10^9</math> FLOPs more than inference from the compressed representation.<br />
<br />
=====Computational Gains on Segmentation=====<br />
<br />
In the figure on the right illustrates, the mIoU validation performance is shown as a function of computational complexity for<br />
the 0.0983 bpp compression operating point. <br />
Here, even without accounting for the decoding cost of the reconstructed images, the compressed representation<br />
performs better. At a fixed computational cost, segmentation from the compressed representation gives about 0.7% better mIoU. And at a fixed mIoU the computational cost is about <math>3.3*10^9</math> FLOPs<br />
lower for compressed representations. Accounting for the decoding costs this difference becomes <math>6.1*10^9</math> FLOPs. due to the nature of the dilated convolutions and the increased feature map size, the<br />
relative computational gains for segmentation are not as pronounced as for classification.<br />
<br />
===Joint Training for Compression and Image Classification===<br />
<br />
==== Training Procedure ====<br />
<br />
When doing joint training, the compression network and the classification networks are first initialized<br />
from a trained state obtained as described previously. After initialization, the networks are<br />
both finetuned jointly. For a detailed<br />
description of hyperparameters used and the training schedule see Appendix A8 in the paper.<br />
<br />
To control that the change in classification accuracy is not only due to (1) a better compression<br />
operating point or (2) the fact that the cResNet is trained longer, the following is done. A new operating point is obtained by finetuning the compression network only using the schedule described<br />
above. The cResNet-51 is trained on top of this new operating point from scratch. Finally, the compression network is fixed at the new operating point, and the cResNet-51 is trained for 9 epochs. <br />
<br />
To obtain segmentation results, the jointly trained network is used. The operating point is fixed and the jointly finetuned classification network is adopted fro segmentation (cResNet-51-d).<br />
<br />
==== Joint Training Results ====<br />
<br />
[[File:AR_Fig7.png|400px|center]]<br />
<br />
It can be seen from the figure, that the classification and segmentation results “move<br />
up” from the baseline through fine tuning. When training jointly the improvement for classification are larger and<br />
a significant improvement for segmentation is achieved. For the 0.635 bpp operating point the classification performance is similar for training the network jointly and training<br />
the compression network only, but when using these operating points for segmentation the difference is considerable.<br />
<br />
The results presented by the authors suggest an improvement in classification by 2%, a performance gain which would<br />
require an additional 75% of the computational complexity of cResNet-51. The segmentation<br />
performance after training the networks jointly is 1.7% better in mIoU than training only<br />
the compression network.<br />
<br />
==Critique==<br />
<br />
The paper proposes how previous work in auto-encoders and image compression can be extended effectively to a novel task of a combined image compression and recognition task. The work has provided extensive experimental evaluation and evidence that suggests that learned compressed representations can be effective in classification and segmentation tasks. While maintaining the performance of the techniques to state of the art performance, the authors show that the proposed method can offer significant computational gains. The applications of this can be in<br />
multimedia communication, wireless transmission of images, video surveillance on the mobile edge, etc. With the advent of 5G and other new wireless technologies, this method offers capabilities that can be utilized to conserve wireless bandwidth, savings on storage while retaining the perceptual quality of images.<br />
The joint training of compression and classification network provides some added advantages and also shows that at aggressive compression rates the performance in classification and segmentation can be improved significantly.<br />
<br />
The authors mention that the complexity of the current approach is still high in comparison with methods like JPEG or JPEG2000. They also mention that this can be overcome when the networks are trained and run on GPU's. Although this has been seen as a drawback, with subsequent improvements in physical hardware and more specialized deep learning platforms, the limitation of the current approach can be overcome. While the authors did thorough experiments and gave extensive results on compressed representations and their advantages, the idea itself is not very novel.Finally, in the light of providing extensive experimental contributions,<br />
the authors have written a quite lengthy paper. There are parts of the paper where the ideas have been repeated frequently, and this could've been avoided leading to a more well-balanced length of the article.<br />
<br />
* ([[https://openreview.net/forum?id=HkXWCMbRW]]) As it is mentioned in the paper, solving a Vision problem directly from a compressed image, is not a novel method (e.g: DCT coefficients were used for both vision and audio data to solve a task without any decompression).<br />
<br />
==Conclusion==<br />
<br />
The paper proposes an inference task using compressed image representations without the need to decode for classification and semantic segmentation. The paper has successfully demonstrated through a set of rigorous experiments the approach<br />
for performing the intended tasks. The results show significant improvements in computational complexity while maintaining state of the art classification and segmentation performance. The authors also intend to explore other computer vision tasks based on using compressed representation as part of the future work. They also suggest that this could potentially lead to gaining a better understanding of the features/compressed representations learned by image compression networks leading to applications in unsupervised or semi-supervised learning.<br />
<br />
==References==<br />
# Torfason, R., Mentzer, F., Agustsson, E., Tschannen, M., Timofte, R., & Van Gool, L. (2018). Towards image understanding from deep compression without decoding. arXiv preprint arXiv:1803.06131.<br />
# Theis, L., Shi, W., Cunningham, A., & Huszár, F. (2017). Lossy image compression with compressive autoencoders. arXiv preprint arXiv:1703.00395.<br />
# Agustsson, E., Mentzer, F., Tschannen, M., Cavigelli, L., Timofte, R., Benini, L., & Gool, L. V. (2017). Soft-to-hard vector quantization for end-to-end learning compressible representations. In Advances in Neural Information Processing Systems (pp. 1141-1151).<br />
# He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 770-778).<br />
# Chen, L. C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2018). Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence, 40(4), 834-848.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fix_your_classifier:_the_marginal_value_of_training_the_last_weight_layer&diff=42218Fix your classifier: the marginal value of training the last weight layer2018-12-02T23:31:50Z<p>A22ravi: /* Using a Hadmard Matrix */</p>
<hr />
<div><br />
The code for the proposed model is available at https://github.com/eladhoffer/fix_your_classifier.<br />
<br />
=Introduction=<br />
<br />
Deep neural networks have become widely used for machine learning, achieving state-of-the-art results on many tasks. One of the most common tasks they are used for is classification. For example, convolutional neural networks (CNNs) are used to classify images to a semantic category. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more computational resources.<br />
<br />
=Brief Overview=<br />
<br />
In order to alleviate the aforementioned problem, the authors propose that the final layer of the classifier be fixed (up to a global scale constant). They argue that with little or no loss of accuracy for most classification tasks, the method provides significant memory and computational benefits. In addition, they show that by initializing the classifier with a Hadamard matrix the inference could be made faster as well.<br />
<br />
=Previous Work=<br />
<br />
Training NN models and using them for inference requires large amounts of memory and computational resources; thus, extensive amount of research has been done lately to reduce the size of networks which are as follows:<br />
<br />
* Weight sharing and specification (Han et al., 2015)<br />
<br />
* Mixed precision to reduce the size of the neural networks by half (Micikevicius et al., 2017)<br />
<br />
* Low-rank approximations to speed up CNN (Tai et al., 2015)<br />
<br />
* Quantization of weights, activations, and gradients to further reduce computation during training (Hubara et al., 2016b; Li et al., 2016 and Zhou et al., 2016). Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
<br />
Some of the past works have also put forward the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on many of the classification tasks. However, the authors' proposal in the current paper suggests the reverse proposal - common Neural Network models used can learn useful representations even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Background=<br />
<br />
A Convolutional Neural Network (CNN) is comprised of one or more convolutional layers (often with a subsampling step) and then followed by one or more fully connected layers as in a standard multilayer neural network. The architecture of a CNN is designed to take advantage of the 2D structure of an input image (or other 2D input such as a speech signal). This is achieved with local connections and tied weights followed by some form of pooling which results in translation invariant features. Another benefit of CNNs is that they are easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. <br />
<br />
A CNN consists of a number of convolutional and subsampling layers optionally followed by fully connected layers. The input to a convolutional layer is a <math>m \times m \times r</math> image where m is the height and width of the image and <math>r</math> is the number of channels, e.g. an RGB image has <math>r=3</math>. The convolutional layer will have <math>k</math> filters (or kernels) of size <math>n \times n \times q</math> where <math>n</math> is smaller than the dimension of the image and <math>q</math> can either be the same as the number of channels <math>r</math> or smaller and may vary for each kernel. The size of the filters gives rise to the locally connected structure which are each convolved with the image to produce <math>k</math> feature maps of size <math>m−n+1</math>. Each map is then subsampled typically with mean or max pooling over <math>p \times p</math> contiguous regions where <math>p</math> ranges between 2 for small images (e.g. MNIST) and is usually not more than 5 for larger inputs. Either before or after the subsampling layer an additive bias and sigmoidal nonlinearity is applied to each feature map. <br />
<br />
CNNs are commonly used to solve a variety of spatial and temporal tasks. Earlier architectures of CNNs (LeCun et al., 1998; Krizhevsky et al., 2012) used a set of fully-connected layers at later stages of the network, presumably to allow classification based on global features of an image.<br />
<br />
<br />
<br />
== Shortcomings of the Final Classification Layer and its Solution ==<br />
<br />
Zeiler & Fergus, 2014 showed that despite the enormous number of trainable parameters these layers add to the model, they are known to have a rather marginal impact on the final performance of the network.<br />
<br />
It has been shown previously that these layers could be easily compressed and reduced after a model was trained by simple means such as matrix decomposition and sparsification (Han et al., 2015). Modern architecture choices are characterized with the removal of most of the fully connected layers (Lin et al., 2013; Szegedy et al., 2015; He et al., 2016), that lead to better generalization and overall accuracy, together with a huge decrease in the number of trainable parameters. Additionally, numerous works showed that CNNs can be trained in a metric learning regime (Bromley et al., 1994; Schroff et al., 2015; Hoffer & Ailon, 2015), where no explicit classification layer was introduced and the objective regarded only distance measures between intermediate representations. Hardt & Ma (2017) suggested an all-convolutional network variant, where they kept the original initialization of the classification layer fixed with no negative impact on performance on the CIFAR-10 dataset.<br />
<br />
=Proposed Method=<br />
<br />
The aforementioned works provide evidence that fully-connected layers are in fact redundant and play a small role in learning and generalization. In this work, the authors have suggested that the parameters used for the final classification transform are completely redundant, and can be replaced with a predetermined linear transform. This holds for even in large-scale models and classification tasks, such as recent architectures trained on the ImageNet benchmark (Deng et al., 2009).<br />
<br />
==Using a Fixed Classifier==<br />
<br />
Suppose the final representation obtained by the network (the last hidden layer) is represented as <math>x = F(z;\theta)</math> where <math>F</math> is assumed to be a deep neural network with input z and parameters θ, e.g., a convolutional network, trained by backpropagation.<br />
<br />
In common NN models, this representation is followed by an additional affine transformation, <math>y = W^T x + b</math> ,where <math>W</math> and <math>b</math> are also trained by back-propagation.<br />
<br />
For input <math>x</math> of <math>N</math> length, and <math>C</math> different possible outputs, <math>W</math> is required to be a matrix of <math>N ×<br />
C</math>. Training is done using cross-entropy loss, by feeding the network outputs through a softmax activation<br />
<br />
<math><br />
v_i = \frac{e^{y_i}}{\sum_{j}^{C}{e^{y_j}}}, i &isin; </math> { <math> {1, . . . , C} </math> }<br />
<br />
and reducing the expected negative log likelihood with respect to ground-truth target <math> t &isin; </math> { <math> {1, . . . , C} </math> },<br />
by minimizing the loss function:<br />
<br />
<math><br />
L(x, t) = −\text{log}\ {v_t} = −{w_t}·{x} − b_t + \text{log} ({\sum_{j}^{C}e^{w_j . x + b_j}})<br />
</math><br />
<br />
where <math>w_i</math> is the <math>i</math>-th column of <math>W</math>.<br />
<br />
==Choosing the Projection Matrix==<br />
<br />
To evaluate the conjecture regarding the importance of the final classification transformation, the trainable parameter matrix <math>W</math> is replaced with a fixed orthonormal projection <math> Q &isin; R^{N×C} </math>, such that <math> &forall; i &ne; j : q_i · q_j = 0 </math> and <math> || q_i ||_{2} = 1 </math>, where <math>q_i</math> is the <math>i</math>th column of <math>Q</math>. This is ensured by a simple random sampling and singular-value decomposition<br />
<br />
As the rows of classifier weight matrix are fixed with an equally valued <math>L_{2}</math> norm, we find it beneficial<br />
to also restrict the representation of <math>x</math> by normalizing it to reside on the <math>n</math>-dimensional sphere:<br />
<br />
<center><math><br />
\hat{x} = \frac{x}{||x||_{2}}<br />
</math></center><br />
<br />
This allows faster training and convergence, as the network does not need to account for changes in the scale of its weights. However, it has now an issue that <math>q_i · \hat{x} </math> is bounded between −1 and 1. This causes convergence issues, as the softmax function is scale sensitive, and the network is affected by the inability to re-scale its input. This issue is amended with a fixed scale <math>T</math> applied to softmax inputs <math>f(y) = softmax(\frac{1}{T}y)</math>, also known as the ''softmax temperature''. However, this introduces an additional hyper-parameter which may differ between networks and datasets. So, the authors propose to introduce a single scalar parameter <math>\alpha</math> to learn the softmax scale, effectively functioning as an inverse of the softmax temperature <math>\frac{1}{T}</math>. The normalized weights and an additional scale coefficient are also used, specially using a single scale for all entries in the weight matrix. The additional vector of bias parameters <math>b &isin; \mathbb{R}^{C}</math> is kept the same and the model is trained using the traditional negative-log-likelihood criterion. Explicitly, the classifier output is now:<br />
<br />
<center><br />
<math><br />
v_i=\frac{e^{\alpha q_i &middot; \hat{x} + b_i}}{\sum_{j}^{C} e^{\alpha q_j &middot; \hat{x} + b_j}}, i &isin; </math> { <math> {1,...,C} </math>}<br />
</center><br />
<br />
and the loss to be minimized is:<br />
<br />
<center><math><br />
L(x, t) = -\alpha q_t &middot; \frac{x}{||x||_{2}} + b_t + \text{log} (\sum_{i=1}^{C} \text{exp}((\alpha q_i &middot; \frac{x}{||x||_{2}} + b_i)))<br />
</math></center><br />
<br />
where <math>x</math> is the final representation obtained by the network for a specific sample, and <math> t &isin; </math> { <math> {1, . . . , C} </math> } is the ground-truth label for that sample. The behaviour of the parameter <math> \alpha </math> over time, which is logarithmic in nature and has the same behavior exhibited by the norm of a learned classifier, is shown in<br />
[[Media: figure1_log_behave.png| Figure 1]].<br />
<br />
<center>[[File:figure1_log_behave.png]]</center><br />
<br />
When <math> -1 \le q_i · \hat{x} \le 1 </math>, a possible cosine angle loss is <br />
<br />
<center>[[File:caloss.png]]</center><br />
<br />
But its final validation accuracy has a slight decrease, compared to original models.<br />
<br />
==Using a Hadamard Matrix==<br />
<br />
To recall, Hadamard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are either +1 or −1. <br />
Example:<br />
<br />
<math>\displaystyle H_{4}={\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\end{bmatrix}}</math><br />
<br />
Furthermore, <math> H </math> is orthogonal, such that <math> HH^{T} = nI_n </math> where <math>I_n</math> is the identity matrix. Instead of using the entire Hadamard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all <math>C</math> rows are orthogonal as the final classification layer is such that:<br />
<br />
<center><math><br />
y = \hat{H} \hat{x} + b<br />
</math></center><br />
<br />
This usage allows two main benefits:<br />
* A deterministic, low-memory and easily generated matrix that can be used for classification.<br />
* Removal of the need to perform a full matrix-matrix multiplication - as multiplying by a Hadamard matrix can be done by simple sign manipulation and addition.<br />
<br />
Here, <math>n</math> must be a multiple of 4, but it can be easily truncated to fit normally defined networks. Also, as the classifier weights are fixed to need only 1-bit precision, it is now possible to focus our attention on the features preceding it.<br />
<br />
=Experimental Results=<br />
<br />
The authors have evaluated their proposed model on the following datasets:<br />
<br />
==CIFAR-10/100==<br />
<br />
===About the Dataset===<br />
<br />
CIFAR-10 is an image classification benchmark dataset containing 50,000 training images and 10,000 test images. The images are in color and contain 32×32 pixels. There are 10 possible classes of various animals and vehicles. CIFAR-100 holds the same number of images of the same size, but contains 100 different classes.<br />
<br />
===Training Details===<br />
<br />
The authors trained a residual network ( He et al., 2016) on the CIFAR-10 dataset. The network depth was 56 and the same hyper-parameters as in the original work were used. A comparison of the two variants, i.e., the learned classifier and the proposed classifier with a fixed transformation is shown in [[Media: figure1_resnet_cifar10.png | Figure 2]].<br />
<br />
<center>[[File: figure1_resnet_cifar10.png]]</center><br />
<br />
These results demonstrate that although the training error is considerably lower for the network with learned classifier, both models achieve the same classification accuracy on the validation set. The authors' conjecture is that with the new fixed parameterization, the network can no longer increase the norm of a given sample’s representation - thus learning its label requires more effort. As this may happen for specific seen samples - it affects only training error.<br />
<br />
The authors also compared using a fixed scale variable <math>\alpha </math> at different values vs. the learned parameter. Results for <math> \alpha = </math> {0.1, 1, 10} are depicted in [[Media: figure3_alpha_resnet_cifar.png| Figure 3]] for both training and validation error and as can be seen, similar validation accuracy can be obtained using a fixed scale value (in this case <math>\alpha </math>= 1 or 10 will suffice) at the expense of another hyper-parameter to seek. In all the further experiments the scaling parameter <math> \alpha </math> was regularized with the same weight decay coefficient used on original classifier. Although learning the scale is not necessary, but it will help convergence during training.<br />
<br />
<center>[[File: figure3_alpha_resnet_cifar.png]]</center><br />
<br />
The authors then train the model on CIFAR-100 dataset. They used the DenseNet-BC model from Huang et al. (2017) with a depth of 100 layers and k = 12. The higher number of classes caused the number of parameters to grow and encompassed about 4% of the whole model. However, validation accuracy for the fixed-classifier model remained equally good as the original model, and the same training curve was observed as earlier.<br />
<br />
==IMAGENET==<br />
<br />
===About the Dataset===<br />
<br />
The Imagenet dataset introduced by Deng et al. (2009) spans over 1000 visual classes, and over 1.2 million samples. This is supposedly a more challenging dataset to work on as compared to CIFAR-10/100.<br />
<br />
===Experiment Details===<br />
<br />
The authors evaluated their fixed classifier method on Imagenet using Resnet50 by He et al. (2016) and Densenet169 model (Huang et al., 2017) as described in the original work. Using a fixed classifier removed approximately 2-million parameters were from the model, accounting for about 8% and 12 % of the model parameters respectively. The experiments revealed similar trends as observed on CIFAR-10.<br />
<br />
For a more stricter evaluation, the authors also trained a Shufflenet architecture (Zhang et al., 2017b), which was designed to be used in low memory and limited computing platforms and has parameters making up the majority of the model. They were able to reduce the parameters to 0.86 million as compared to 0.96 million parameters in the final layer of the original model. Again, the proposed modification in the original model gave similar convergence results on validation accuracy. Interestingly, this method allowed Imagenet training in an under-specified regime, where there are<br />
more training samples than the number of parameters. This is an unconventional regime for modern deep networks, which are usually over-specified to have many more parameters than training samples (Zhang et al., 2017a).<br />
<br />
The overall results of the fixed-classifier are summarized in [[Media: table1_fixed_results.png | Table 1]].<br />
<br />
<center>[[File: table1_fixed_results.png]]</center><br />
<br />
==Language Modelling==<br />
<br />
Recent works have empirically found that using the same weights for both word embedding and classifier can yield equal or better results than using a separate pair of weights. So the authors experimented with fix-classifiers on language modeling as it also requires classification of all possible tokens available in the task vocabulary. They trained a recurrent model with 2-layers of LSTM (Hochreiter & Schmidhuber, 1997) and embedding + hidden size of 512 on the WikiText2 dataset (Merity et al., 2016), using same settings as in Merity et al. (2017). WikiText2 dataset contains about 33K different words, so the number of parameters expected in the embedding and classifier layer was about 34-million. This number is about 89% of the total number of parameters used for the whole model which is 38-million. However, using a random orthogonal transform yielded poor results compared to learned embedding. This was suspected to be due to semantic relationships captured in the embedding layer of language models, which is not the case in image classification task. The intuition was further confirmed by the much better results when pre-trained embeddings using word2vec algorithm by Mikolov et al. (2013) or PMI factorization as suggested by Levy & Goldberg (2014), were used. The final result used 89% fewer parameters than a fully learned model, with only marginally worse perplexity. The authors posit that this implies a required structure in word embedding that originates from the semantic relatedness between words, and unbalanced classes. They further suggest that with more efficient ways to train word embeddings, it may be possible to mitigate the issues arising from this structure and class imbalance. <br />
<br />
<center>[[File: language.png]]</center><br />
<br />
=Discussion=<br />
<br />
==Implications and Use Cases==<br />
<br />
With the increasing number of classes in the benchmark datasets, computational demands for the final classifier will increase as well. In order to understand the problem better, the authors observe the work by Sun et al. (2017), which introduced JFT-300M - an internal Google dataset with over 18K different classes. Using a Resnet50 (He et al., 2016), with a 2048 sized representation led to a model with over 36M parameters meaning that over 60% of the model parameters resided in the final classification layer. Sun et al. (2017) also describe the difficulty in distributing so many parameters over the training servers involving a non-trivial overhead during synchronization of the model for update. The authors claim that the fixed-classifier would help considerably in this kind of scenario - where using a fixed classifier removes the need to do any gradient synchronization for the final layer. Furthermore, introduction of Hadamard matrix removes the need to save the transformation altogether, thereby, making it more efficient and allowing considerable memory and computational savings.<br />
<br />
==Possible Caveats==<br />
<br />
The good performance of fixed-classifiers relies on the ability of the preceding layers to learn separable representations. This could be affected when the ratio between learned features and number of classes is small – that is, when <math> C > N</math>. However, they tested their method in such cases and their model performed well and provided good results.<br />
Another factor that can affect the performance of their model using a fixed classifier is when the classes are highly correlated. In that case, the fixed classifier actually cannot support correlated classes and thus, the network could have some difficulty to learn. For a language model, word classes tend to have highly correlated instances, which also lead to difficult learning process.<br />
<br />
Also, this proposed approach will only eliminate the computation of the classifier weights, so when the classes are fewer, the computation saving effect will not be readily apparent.<br />
<br />
==Future Work==<br />
<br />
<br />
The use of fixed classifiers might be further simplified in Binarized Neural Networks (Hubara et al., 2016a), where the activations and weights are restricted to ±1 during propagations. In that case, the norm of the last hidden layer would be constant for all samples (equal to the square root of the hidden layer width). The constant could then be absorbed into the scale constant <math>\alpha</math>, and there is no need in a per-sample normalization.<br />
<br />
Additionally, more efficient ways to learn a word embedding should also be explored where similar redundancy in classifier weights may suggest simpler forms of token representations - such as low-rank or sparse versions.<br />
<br />
A related paper was published that claims that fixing most of the parameters of the neural network achieves comparable results with learning all of them [A. Rosenfeld and J. K. Tsotsos]<br />
<br />
=Conclusion=<br />
<br />
In this work, the authors argue that the final classification layer in deep neural networks is redundant and suggest removing the parameters from the classification layer. The empirical results from experiments on the CIFAR and IMAGENET datasets suggest that such a change lead to little or almost no decline in the performance of the architecture. Furthermore, using a Hadmard matrix as classifier might lead to some computational benefits when properly implemented, and save memory otherwise spent on large amount of transformation coefficients.<br />
<br />
Another possible scope of research that could be pointed out for future could be to find new efficient methods to create pre-defined word embeddings, which require huge amount of parameters that can possibly be avoided when learning a new task. Therefore, more emphasis should be given to the representations learned by the non-linear parts of the neural networks - up to the final classifier, as it seems highly redundant.<br />
<br />
=Critique=<br />
<br />
The paper proposes an interesting idea that has a potential use case when designing memory-efficient neural networks. The experiments shown in the paper are quite rigorous and provide support to the authors' claim. However, it would have been more helpful if the authors had described a bit more about efficient implementation of the Hadamard matrix and how to scale this method for larger datasets (cases with <math> C >N</math>).<br />
<br />
Moreover, one of the main intuitions of the paper has introduced to be computational cost but it has left out to compare a fixed and learned classifier based on the computational cost and then investigate whether it worth the drop in performance or not considering the fact that not always the output can be degraded because of need for speed! At least a discussion on this issue is expected.<br />
<br />
On the other hand, the computational cost and performance change after fixation of classifier could be related to dataset and the nature and complexity of it. Mostly, having 1000 classes makes the classification more crucial than 2 classes. An evaluation of this topic is also needed.<br />
<br />
Another interesting experiment to do would be to look this technique interacts with distillation when used in the teacher or student network or both. For instance, Does fixing the features make it more difficult to place dog than on boat when classifying a cat? Do networks with fixed classifier weights make worse teachers for distillation?<br />
<br />
=References=<br />
<br />
Madhu S Advani and Andrew M Saxe. High-dimensional dynamics of generalization error in neural networks. arXiv preprint arXiv:1710.03667, 2017.<br />
<br />
Peter Bartlett, Dylan J Foster, and Matus Telgarsky. Spectrally-normalized margin bounds for neural networks. arXiv preprint arXiv:1706.08498, 2017.<br />
<br />
Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Sackinger, and Roopak Shah. Signature verification using a” siamese” time delay neural network. In Advances in Neural Information Processing Systems, pp. 737–744, 1994.<br />
<br />
Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Binaryconnect: Training deep neural networks with binary weights during propagations. In Advances in Neural Information Processing Systems, pp. 3123–3131, 2015.<br />
<br />
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 248–255. IEEE, 2009.<br />
<br />
Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro. Implicit regularization in matrix factorization. arXiv preprint arXiv:1705.09280, 2017.<br />
<br />
Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.<br />
<br />
Moritz Hardt and Tengyu Ma. Identity matters in deep learning. 2017.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.<br />
<br />
A Hedayat, WD Wallis, et al. Hadamard matrices and their applications. The Annals of Statistics, 6<br />
(6):1184–1238, 1978.<br />
<br />
Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.<br />
<br />
Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International Workshop on Similarity-Based Pattern Recognition, pp. 84–92. Springer, 2015.<br />
<br />
Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. 2017.<br />
<br />
Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017.<br />
<br />
Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017.<br />
<br />
Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew. Extreme learning machine: theory and applications. Neurocomputing, 70(1):489–501, 2006.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. In Advances in Neural Information Processing Systems 29 (NIPS’16), 2016a.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Quantized neural networks: Training neural networks with low precision weights and activations. arXiv preprint arXiv:1609.07061, 2016b.<br />
<br />
Hakan Inan, Khashayar Khosravi, and Richard Socher. Tying word vectors and word classifiers: A loss framework for language modeling. arXiv preprint arXiv:1611.01462, 2016.<br />
<br />
Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. arXiv preprint arXiv:1405.3866, 2014.<br />
<br />
Alex Krizhevsky. Learning multiple layers of features from tiny images. 2009.<br />
<br />
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012.<br />
<br />
Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278 2324, 1998.<br />
<br />
Omer Levy and Yoav Goldberg. Neural word embedding as implicit matrix factorization. In Advances in neural information processing systems, pp. 2177–2185, 2014.<br />
<br />
Fengfu Li, Bo Zhang, and Bin Liu. Ternary weight networks. arXiv preprint arXiv:1605.04711, 2016.<br />
<br />
Min Lin, Qiang Chen, and Shuicheng Yan. Network in network. arXiv preprint arXiv:1312.4400, 2013.<br />
<br />
Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. arXiv preprint arXiv:1609.07843, 2016.<br />
<br />
Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017.<br />
<br />
Paulius Micikevicius, Sharan Narang, Jonah Alben, Gregory Diamos, Erich Elsen, David Garcia, Boris Ginsburg, Michael Houston, Oleksii Kuchaev, Ganesh Venkatesh, et al. Mixed precision training. arXiv preprint arXiv:1710.03740, 2017.<br />
<br />
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed tations of words and phrases and their compositionality. In Advances in neural information processing systems, pp. 3111–3119, 2013.<br />
<br />
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring generalization in deep learning. arXiv preprint arXiv:1706.08947, 2017.<br />
Jooyoung Park and Irwin W Sandberg. Universal approximation using radial-basis-function networks. Neural computation, 3(2):246–257, 1991.<br />
<br />
Ofir Press and Lior Wolf. Using the output embedding to improve language models. EACL 2017,<br />
pp. 157, 2017.<br />
<br />
Itay Safran and Ohad Shamir. On the quality of the initial basin in overspecified neural networks. In International Conference on Machine Learning, pp. 774–782, 2016.<br />
<br />
Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016.<br />
<br />
Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 815–823, 2015.<br />
<br />
Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. arXiv preprint arXiv:1707.04926, 2017.<br />
<br />
Daniel Soudry and Yair Carmon. No bad local minima: Data independent training error guarantees for multilayer neural networks. arXiv preprint arXiv:1605.08361, 2016.<br />
<br />
Daniel Soudry and Elad Hoffer. Exponentially vanishing sub-optimal local minima in multilayer neural networks. arXiv preprint arXiv:1702.05777, 2017.<br />
<br />
Daniel Soudry, Elad Hoffer, and Nathan Srebro. The implicit bias of gradient descent on separable data. 2018.<br />
<br />
Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.<br />
<br />
Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. arXiv preprint arXiv:1707.02968, 2017.<br />
<br />
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1–9, 2015.<br />
<br />
Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2818–2826, 2016.<br />
<br />
Cheng Tai, Tong Xiao, Yi Zhang, Xiaogang Wang, et al. Convolutional neural networks with lowrank regularization. arXiv preprint arXiv:1511.06067, 2015.<br />
<br />
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2017.<br />
Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
Bo Xie, Yingyu Liang, and Le Song. Diversity leads to generalization in neural networks. arXiv preprint arXiv:1611.03131, 2016.<br />
<br />
Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European conference on computer vision, pp. 818–833. Springer, 2014. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017a. URL https://arxiv.org/abs/1611.03530.<br />
<br />
Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. arXiv preprint arXiv:1707.01083, 2017b.<br />
<br />
Shuchang Zhou, Zekun Ni, Xinyu Zhou, He Wen, Yuxin Wu, and Yuheng Zou. Dorefa-net: Training low bitwidth convolutional neural networks with low bitwidth gradients. arXiv preprint arXiv:1606.06160, 2016.<br />
<br />
A. Rosenfeld and J. K. Tsotsos, “Intriguing properties of randomly weighted networks: Generalizing while learning next to nothing,” arXiv preprint arXiv:1802.00844, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fix_your_classifier:_the_marginal_value_of_training_the_last_weight_layer&diff=42217Fix your classifier: the marginal value of training the last weight layer2018-12-02T23:31:30Z<p>A22ravi: /* Using a Hadmard Matrix */</p>
<hr />
<div><br />
The code for the proposed model is available at https://github.com/eladhoffer/fix_your_classifier.<br />
<br />
=Introduction=<br />
<br />
Deep neural networks have become widely used for machine learning, achieving state-of-the-art results on many tasks. One of the most common tasks they are used for is classification. For example, convolutional neural networks (CNNs) are used to classify images to a semantic category. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more computational resources.<br />
<br />
=Brief Overview=<br />
<br />
In order to alleviate the aforementioned problem, the authors propose that the final layer of the classifier be fixed (up to a global scale constant). They argue that with little or no loss of accuracy for most classification tasks, the method provides significant memory and computational benefits. In addition, they show that by initializing the classifier with a Hadamard matrix the inference could be made faster as well.<br />
<br />
=Previous Work=<br />
<br />
Training NN models and using them for inference requires large amounts of memory and computational resources; thus, extensive amount of research has been done lately to reduce the size of networks which are as follows:<br />
<br />
* Weight sharing and specification (Han et al., 2015)<br />
<br />
* Mixed precision to reduce the size of the neural networks by half (Micikevicius et al., 2017)<br />
<br />
* Low-rank approximations to speed up CNN (Tai et al., 2015)<br />
<br />
* Quantization of weights, activations, and gradients to further reduce computation during training (Hubara et al., 2016b; Li et al., 2016 and Zhou et al., 2016). Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
<br />
Some of the past works have also put forward the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on many of the classification tasks. However, the authors' proposal in the current paper suggests the reverse proposal - common Neural Network models used can learn useful representations even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Background=<br />
<br />
A Convolutional Neural Network (CNN) is comprised of one or more convolutional layers (often with a subsampling step) and then followed by one or more fully connected layers as in a standard multilayer neural network. The architecture of a CNN is designed to take advantage of the 2D structure of an input image (or other 2D input such as a speech signal). This is achieved with local connections and tied weights followed by some form of pooling which results in translation invariant features. Another benefit of CNNs is that they are easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. <br />
<br />
A CNN consists of a number of convolutional and subsampling layers optionally followed by fully connected layers. The input to a convolutional layer is a <math>m \times m \times r</math> image where m is the height and width of the image and <math>r</math> is the number of channels, e.g. an RGB image has <math>r=3</math>. The convolutional layer will have <math>k</math> filters (or kernels) of size <math>n \times n \times q</math> where <math>n</math> is smaller than the dimension of the image and <math>q</math> can either be the same as the number of channels <math>r</math> or smaller and may vary for each kernel. The size of the filters gives rise to the locally connected structure which are each convolved with the image to produce <math>k</math> feature maps of size <math>m−n+1</math>. Each map is then subsampled typically with mean or max pooling over <math>p \times p</math> contiguous regions where <math>p</math> ranges between 2 for small images (e.g. MNIST) and is usually not more than 5 for larger inputs. Either before or after the subsampling layer an additive bias and sigmoidal nonlinearity is applied to each feature map. <br />
<br />
CNNs are commonly used to solve a variety of spatial and temporal tasks. Earlier architectures of CNNs (LeCun et al., 1998; Krizhevsky et al., 2012) used a set of fully-connected layers at later stages of the network, presumably to allow classification based on global features of an image.<br />
<br />
<br />
<br />
== Shortcomings of the Final Classification Layer and its Solution ==<br />
<br />
Zeiler & Fergus, 2014 showed that despite the enormous number of trainable parameters these layers add to the model, they are known to have a rather marginal impact on the final performance of the network.<br />
<br />
It has been shown previously that these layers could be easily compressed and reduced after a model was trained by simple means such as matrix decomposition and sparsification (Han et al., 2015). Modern architecture choices are characterized with the removal of most of the fully connected layers (Lin et al., 2013; Szegedy et al., 2015; He et al., 2016), that lead to better generalization and overall accuracy, together with a huge decrease in the number of trainable parameters. Additionally, numerous works showed that CNNs can be trained in a metric learning regime (Bromley et al., 1994; Schroff et al., 2015; Hoffer & Ailon, 2015), where no explicit classification layer was introduced and the objective regarded only distance measures between intermediate representations. Hardt & Ma (2017) suggested an all-convolutional network variant, where they kept the original initialization of the classification layer fixed with no negative impact on performance on the CIFAR-10 dataset.<br />
<br />
=Proposed Method=<br />
<br />
The aforementioned works provide evidence that fully-connected layers are in fact redundant and play a small role in learning and generalization. In this work, the authors have suggested that the parameters used for the final classification transform are completely redundant, and can be replaced with a predetermined linear transform. This holds for even in large-scale models and classification tasks, such as recent architectures trained on the ImageNet benchmark (Deng et al., 2009).<br />
<br />
==Using a Fixed Classifier==<br />
<br />
Suppose the final representation obtained by the network (the last hidden layer) is represented as <math>x = F(z;\theta)</math> where <math>F</math> is assumed to be a deep neural network with input z and parameters θ, e.g., a convolutional network, trained by backpropagation.<br />
<br />
In common NN models, this representation is followed by an additional affine transformation, <math>y = W^T x + b</math> ,where <math>W</math> and <math>b</math> are also trained by back-propagation.<br />
<br />
For input <math>x</math> of <math>N</math> length, and <math>C</math> different possible outputs, <math>W</math> is required to be a matrix of <math>N ×<br />
C</math>. Training is done using cross-entropy loss, by feeding the network outputs through a softmax activation<br />
<br />
<math><br />
v_i = \frac{e^{y_i}}{\sum_{j}^{C}{e^{y_j}}}, i &isin; </math> { <math> {1, . . . , C} </math> }<br />
<br />
and reducing the expected negative log likelihood with respect to ground-truth target <math> t &isin; </math> { <math> {1, . . . , C} </math> },<br />
by minimizing the loss function:<br />
<br />
<math><br />
L(x, t) = −\text{log}\ {v_t} = −{w_t}·{x} − b_t + \text{log} ({\sum_{j}^{C}e^{w_j . x + b_j}})<br />
</math><br />
<br />
where <math>w_i</math> is the <math>i</math>-th column of <math>W</math>.<br />
<br />
==Choosing the Projection Matrix==<br />
<br />
To evaluate the conjecture regarding the importance of the final classification transformation, the trainable parameter matrix <math>W</math> is replaced with a fixed orthonormal projection <math> Q &isin; R^{N×C} </math>, such that <math> &forall; i &ne; j : q_i · q_j = 0 </math> and <math> || q_i ||_{2} = 1 </math>, where <math>q_i</math> is the <math>i</math>th column of <math>Q</math>. This is ensured by a simple random sampling and singular-value decomposition<br />
<br />
As the rows of classifier weight matrix are fixed with an equally valued <math>L_{2}</math> norm, we find it beneficial<br />
to also restrict the representation of <math>x</math> by normalizing it to reside on the <math>n</math>-dimensional sphere:<br />
<br />
<center><math><br />
\hat{x} = \frac{x}{||x||_{2}}<br />
</math></center><br />
<br />
This allows faster training and convergence, as the network does not need to account for changes in the scale of its weights. However, it has now an issue that <math>q_i · \hat{x} </math> is bounded between −1 and 1. This causes convergence issues, as the softmax function is scale sensitive, and the network is affected by the inability to re-scale its input. This issue is amended with a fixed scale <math>T</math> applied to softmax inputs <math>f(y) = softmax(\frac{1}{T}y)</math>, also known as the ''softmax temperature''. However, this introduces an additional hyper-parameter which may differ between networks and datasets. So, the authors propose to introduce a single scalar parameter <math>\alpha</math> to learn the softmax scale, effectively functioning as an inverse of the softmax temperature <math>\frac{1}{T}</math>. The normalized weights and an additional scale coefficient are also used, specially using a single scale for all entries in the weight matrix. The additional vector of bias parameters <math>b &isin; \mathbb{R}^{C}</math> is kept the same and the model is trained using the traditional negative-log-likelihood criterion. Explicitly, the classifier output is now:<br />
<br />
<center><br />
<math><br />
v_i=\frac{e^{\alpha q_i &middot; \hat{x} + b_i}}{\sum_{j}^{C} e^{\alpha q_j &middot; \hat{x} + b_j}}, i &isin; </math> { <math> {1,...,C} </math>}<br />
</center><br />
<br />
and the loss to be minimized is:<br />
<br />
<center><math><br />
L(x, t) = -\alpha q_t &middot; \frac{x}{||x||_{2}} + b_t + \text{log} (\sum_{i=1}^{C} \text{exp}((\alpha q_i &middot; \frac{x}{||x||_{2}} + b_i)))<br />
</math></center><br />
<br />
where <math>x</math> is the final representation obtained by the network for a specific sample, and <math> t &isin; </math> { <math> {1, . . . , C} </math> } is the ground-truth label for that sample. The behaviour of the parameter <math> \alpha </math> over time, which is logarithmic in nature and has the same behavior exhibited by the norm of a learned classifier, is shown in<br />
[[Media: figure1_log_behave.png| Figure 1]].<br />
<br />
<center>[[File:figure1_log_behave.png]]</center><br />
<br />
When <math> -1 \le q_i · \hat{x} \le 1 </math>, a possible cosine angle loss is <br />
<br />
<center>[[File:caloss.png]]</center><br />
<br />
But its final validation accuracy has a slight decrease, compared to original models.<br />
<br />
==Using a Hadmard Matrix==<br />
<br />
To recall, Hadmard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are either +1 or −1. <br />
Example:<br />
<br />
<math>\displaystyle H_{4}={\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\end{bmatrix}}</math><br />
<br />
Furthermore, <math> H </math> is orthogonal, such that <math> HH^{T} = nI_n </math> where <math>I_n</math> is the identity matrix. Instead of using the entire Hadmard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all <math>C</math> rows are orthogonal as the final classification layer is such that:<br />
<br />
<center><math><br />
y = \hat{H} \hat{x} + b<br />
</math></center><br />
<br />
This usage allows two main benefits:<br />
* A deterministic, low-memory and easily generated matrix that can be used for classification.<br />
* Removal of the need to perform a full matrix-matrix multiplication - as multiplying by a Hadamard matrix can be done by simple sign manipulation and addition.<br />
<br />
Here, <math>n</math> must be a multiple of 4, but it can be easily truncated to fit normally defined networks. Also, as the classifier weights are fixed to need only 1-bit precision, it is now possible to focus our attention on the features preceding it.<br />
<br />
=Experimental Results=<br />
<br />
The authors have evaluated their proposed model on the following datasets:<br />
<br />
==CIFAR-10/100==<br />
<br />
===About the Dataset===<br />
<br />
CIFAR-10 is an image classification benchmark dataset containing 50,000 training images and 10,000 test images. The images are in color and contain 32×32 pixels. There are 10 possible classes of various animals and vehicles. CIFAR-100 holds the same number of images of the same size, but contains 100 different classes.<br />
<br />
===Training Details===<br />
<br />
The authors trained a residual network ( He et al., 2016) on the CIFAR-10 dataset. The network depth was 56 and the same hyper-parameters as in the original work were used. A comparison of the two variants, i.e., the learned classifier and the proposed classifier with a fixed transformation is shown in [[Media: figure1_resnet_cifar10.png | Figure 2]].<br />
<br />
<center>[[File: figure1_resnet_cifar10.png]]</center><br />
<br />
These results demonstrate that although the training error is considerably lower for the network with learned classifier, both models achieve the same classification accuracy on the validation set. The authors' conjecture is that with the new fixed parameterization, the network can no longer increase the norm of a given sample’s representation - thus learning its label requires more effort. As this may happen for specific seen samples - it affects only training error.<br />
<br />
The authors also compared using a fixed scale variable <math>\alpha </math> at different values vs. the learned parameter. Results for <math> \alpha = </math> {0.1, 1, 10} are depicted in [[Media: figure3_alpha_resnet_cifar.png| Figure 3]] for both training and validation error and as can be seen, similar validation accuracy can be obtained using a fixed scale value (in this case <math>\alpha </math>= 1 or 10 will suffice) at the expense of another hyper-parameter to seek. In all the further experiments the scaling parameter <math> \alpha </math> was regularized with the same weight decay coefficient used on original classifier. Although learning the scale is not necessary, but it will help convergence during training.<br />
<br />
<center>[[File: figure3_alpha_resnet_cifar.png]]</center><br />
<br />
The authors then train the model on CIFAR-100 dataset. They used the DenseNet-BC model from Huang et al. (2017) with a depth of 100 layers and k = 12. The higher number of classes caused the number of parameters to grow and encompassed about 4% of the whole model. However, validation accuracy for the fixed-classifier model remained equally good as the original model, and the same training curve was observed as earlier.<br />
<br />
==IMAGENET==<br />
<br />
===About the Dataset===<br />
<br />
The Imagenet dataset introduced by Deng et al. (2009) spans over 1000 visual classes, and over 1.2 million samples. This is supposedly a more challenging dataset to work on as compared to CIFAR-10/100.<br />
<br />
===Experiment Details===<br />
<br />
The authors evaluated their fixed classifier method on Imagenet using Resnet50 by He et al. (2016) and Densenet169 model (Huang et al., 2017) as described in the original work. Using a fixed classifier removed approximately 2-million parameters were from the model, accounting for about 8% and 12 % of the model parameters respectively. The experiments revealed similar trends as observed on CIFAR-10.<br />
<br />
For a more stricter evaluation, the authors also trained a Shufflenet architecture (Zhang et al., 2017b), which was designed to be used in low memory and limited computing platforms and has parameters making up the majority of the model. They were able to reduce the parameters to 0.86 million as compared to 0.96 million parameters in the final layer of the original model. Again, the proposed modification in the original model gave similar convergence results on validation accuracy. Interestingly, this method allowed Imagenet training in an under-specified regime, where there are<br />
more training samples than the number of parameters. This is an unconventional regime for modern deep networks, which are usually over-specified to have many more parameters than training samples (Zhang et al., 2017a).<br />
<br />
The overall results of the fixed-classifier are summarized in [[Media: table1_fixed_results.png | Table 1]].<br />
<br />
<center>[[File: table1_fixed_results.png]]</center><br />
<br />
==Language Modelling==<br />
<br />
Recent works have empirically found that using the same weights for both word embedding and classifier can yield equal or better results than using a separate pair of weights. So the authors experimented with fix-classifiers on language modeling as it also requires classification of all possible tokens available in the task vocabulary. They trained a recurrent model with 2-layers of LSTM (Hochreiter & Schmidhuber, 1997) and embedding + hidden size of 512 on the WikiText2 dataset (Merity et al., 2016), using same settings as in Merity et al. (2017). WikiText2 dataset contains about 33K different words, so the number of parameters expected in the embedding and classifier layer was about 34-million. This number is about 89% of the total number of parameters used for the whole model which is 38-million. However, using a random orthogonal transform yielded poor results compared to learned embedding. This was suspected to be due to semantic relationships captured in the embedding layer of language models, which is not the case in image classification task. The intuition was further confirmed by the much better results when pre-trained embeddings using word2vec algorithm by Mikolov et al. (2013) or PMI factorization as suggested by Levy & Goldberg (2014), were used. The final result used 89% fewer parameters than a fully learned model, with only marginally worse perplexity. The authors posit that this implies a required structure in word embedding that originates from the semantic relatedness between words, and unbalanced classes. They further suggest that with more efficient ways to train word embeddings, it may be possible to mitigate the issues arising from this structure and class imbalance. <br />
<br />
<center>[[File: language.png]]</center><br />
<br />
=Discussion=<br />
<br />
==Implications and Use Cases==<br />
<br />
With the increasing number of classes in the benchmark datasets, computational demands for the final classifier will increase as well. In order to understand the problem better, the authors observe the work by Sun et al. (2017), which introduced JFT-300M - an internal Google dataset with over 18K different classes. Using a Resnet50 (He et al., 2016), with a 2048 sized representation led to a model with over 36M parameters meaning that over 60% of the model parameters resided in the final classification layer. Sun et al. (2017) also describe the difficulty in distributing so many parameters over the training servers involving a non-trivial overhead during synchronization of the model for update. The authors claim that the fixed-classifier would help considerably in this kind of scenario - where using a fixed classifier removes the need to do any gradient synchronization for the final layer. Furthermore, introduction of Hadamard matrix removes the need to save the transformation altogether, thereby, making it more efficient and allowing considerable memory and computational savings.<br />
<br />
==Possible Caveats==<br />
<br />
The good performance of fixed-classifiers relies on the ability of the preceding layers to learn separable representations. This could be affected when the ratio between learned features and number of classes is small – that is, when <math> C > N</math>. However, they tested their method in such cases and their model performed well and provided good results.<br />
Another factor that can affect the performance of their model using a fixed classifier is when the classes are highly correlated. In that case, the fixed classifier actually cannot support correlated classes and thus, the network could have some difficulty to learn. For a language model, word classes tend to have highly correlated instances, which also lead to difficult learning process.<br />
<br />
Also, this proposed approach will only eliminate the computation of the classifier weights, so when the classes are fewer, the computation saving effect will not be readily apparent.<br />
<br />
==Future Work==<br />
<br />
<br />
The use of fixed classifiers might be further simplified in Binarized Neural Networks (Hubara et al., 2016a), where the activations and weights are restricted to ±1 during propagations. In that case, the norm of the last hidden layer would be constant for all samples (equal to the square root of the hidden layer width). The constant could then be absorbed into the scale constant <math>\alpha</math>, and there is no need in a per-sample normalization.<br />
<br />
Additionally, more efficient ways to learn a word embedding should also be explored where similar redundancy in classifier weights may suggest simpler forms of token representations - such as low-rank or sparse versions.<br />
<br />
A related paper was published that claims that fixing most of the parameters of the neural network achieves comparable results with learning all of them [A. Rosenfeld and J. K. Tsotsos]<br />
<br />
=Conclusion=<br />
<br />
In this work, the authors argue that the final classification layer in deep neural networks is redundant and suggest removing the parameters from the classification layer. The empirical results from experiments on the CIFAR and IMAGENET datasets suggest that such a change lead to little or almost no decline in the performance of the architecture. Furthermore, using a Hadmard matrix as classifier might lead to some computational benefits when properly implemented, and save memory otherwise spent on large amount of transformation coefficients.<br />
<br />
Another possible scope of research that could be pointed out for future could be to find new efficient methods to create pre-defined word embeddings, which require huge amount of parameters that can possibly be avoided when learning a new task. Therefore, more emphasis should be given to the representations learned by the non-linear parts of the neural networks - up to the final classifier, as it seems highly redundant.<br />
<br />
=Critique=<br />
<br />
The paper proposes an interesting idea that has a potential use case when designing memory-efficient neural networks. The experiments shown in the paper are quite rigorous and provide support to the authors' claim. However, it would have been more helpful if the authors had described a bit more about efficient implementation of the Hadamard matrix and how to scale this method for larger datasets (cases with <math> C >N</math>).<br />
<br />
Moreover, one of the main intuitions of the paper has introduced to be computational cost but it has left out to compare a fixed and learned classifier based on the computational cost and then investigate whether it worth the drop in performance or not considering the fact that not always the output can be degraded because of need for speed! At least a discussion on this issue is expected.<br />
<br />
On the other hand, the computational cost and performance change after fixation of classifier could be related to dataset and the nature and complexity of it. Mostly, having 1000 classes makes the classification more crucial than 2 classes. An evaluation of this topic is also needed.<br />
<br />
Another interesting experiment to do would be to look this technique interacts with distillation when used in the teacher or student network or both. For instance, Does fixing the features make it more difficult to place dog than on boat when classifying a cat? Do networks with fixed classifier weights make worse teachers for distillation?<br />
<br />
=References=<br />
<br />
Madhu S Advani and Andrew M Saxe. High-dimensional dynamics of generalization error in neural networks. arXiv preprint arXiv:1710.03667, 2017.<br />
<br />
Peter Bartlett, Dylan J Foster, and Matus Telgarsky. Spectrally-normalized margin bounds for neural networks. arXiv preprint arXiv:1706.08498, 2017.<br />
<br />
Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Sackinger, and Roopak Shah. Signature verification using a” siamese” time delay neural network. In Advances in Neural Information Processing Systems, pp. 737–744, 1994.<br />
<br />
Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Binaryconnect: Training deep neural networks with binary weights during propagations. In Advances in Neural Information Processing Systems, pp. 3123–3131, 2015.<br />
<br />
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 248–255. IEEE, 2009.<br />
<br />
Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro. Implicit regularization in matrix factorization. arXiv preprint arXiv:1705.09280, 2017.<br />
<br />
Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.<br />
<br />
Moritz Hardt and Tengyu Ma. Identity matters in deep learning. 2017.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.<br />
<br />
A Hedayat, WD Wallis, et al. Hadamard matrices and their applications. The Annals of Statistics, 6<br />
(6):1184–1238, 1978.<br />
<br />
Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.<br />
<br />
Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International Workshop on Similarity-Based Pattern Recognition, pp. 84–92. Springer, 2015.<br />
<br />
Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. 2017.<br />
<br />
Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017.<br />
<br />
Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017.<br />
<br />
Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew. Extreme learning machine: theory and applications. Neurocomputing, 70(1):489–501, 2006.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. In Advances in Neural Information Processing Systems 29 (NIPS’16), 2016a.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Quantized neural networks: Training neural networks with low precision weights and activations. arXiv preprint arXiv:1609.07061, 2016b.<br />
<br />
Hakan Inan, Khashayar Khosravi, and Richard Socher. Tying word vectors and word classifiers: A loss framework for language modeling. arXiv preprint arXiv:1611.01462, 2016.<br />
<br />
Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. arXiv preprint arXiv:1405.3866, 2014.<br />
<br />
Alex Krizhevsky. Learning multiple layers of features from tiny images. 2009.<br />
<br />
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012.<br />
<br />
Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278 2324, 1998.<br />
<br />
Omer Levy and Yoav Goldberg. Neural word embedding as implicit matrix factorization. In Advances in neural information processing systems, pp. 2177–2185, 2014.<br />
<br />
Fengfu Li, Bo Zhang, and Bin Liu. Ternary weight networks. arXiv preprint arXiv:1605.04711, 2016.<br />
<br />
Min Lin, Qiang Chen, and Shuicheng Yan. Network in network. arXiv preprint arXiv:1312.4400, 2013.<br />
<br />
Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. arXiv preprint arXiv:1609.07843, 2016.<br />
<br />
Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017.<br />
<br />
Paulius Micikevicius, Sharan Narang, Jonah Alben, Gregory Diamos, Erich Elsen, David Garcia, Boris Ginsburg, Michael Houston, Oleksii Kuchaev, Ganesh Venkatesh, et al. Mixed precision training. arXiv preprint arXiv:1710.03740, 2017.<br />
<br />
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed tations of words and phrases and their compositionality. In Advances in neural information processing systems, pp. 3111–3119, 2013.<br />
<br />
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring generalization in deep learning. arXiv preprint arXiv:1706.08947, 2017.<br />
Jooyoung Park and Irwin W Sandberg. Universal approximation using radial-basis-function networks. Neural computation, 3(2):246–257, 1991.<br />
<br />
Ofir Press and Lior Wolf. Using the output embedding to improve language models. EACL 2017,<br />
pp. 157, 2017.<br />
<br />
Itay Safran and Ohad Shamir. On the quality of the initial basin in overspecified neural networks. In International Conference on Machine Learning, pp. 774–782, 2016.<br />
<br />
Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016.<br />
<br />
Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 815–823, 2015.<br />
<br />
Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. arXiv preprint arXiv:1707.04926, 2017.<br />
<br />
Daniel Soudry and Yair Carmon. No bad local minima: Data independent training error guarantees for multilayer neural networks. arXiv preprint arXiv:1605.08361, 2016.<br />
<br />
Daniel Soudry and Elad Hoffer. Exponentially vanishing sub-optimal local minima in multilayer neural networks. arXiv preprint arXiv:1702.05777, 2017.<br />
<br />
Daniel Soudry, Elad Hoffer, and Nathan Srebro. The implicit bias of gradient descent on separable data. 2018.<br />
<br />
Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.<br />
<br />
Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. arXiv preprint arXiv:1707.02968, 2017.<br />
<br />
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1–9, 2015.<br />
<br />
Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2818–2826, 2016.<br />
<br />
Cheng Tai, Tong Xiao, Yi Zhang, Xiaogang Wang, et al. Convolutional neural networks with lowrank regularization. arXiv preprint arXiv:1511.06067, 2015.<br />
<br />
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2017.<br />
Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
Bo Xie, Yingyu Liang, and Le Song. Diversity leads to generalization in neural networks. arXiv preprint arXiv:1611.03131, 2016.<br />
<br />
Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European conference on computer vision, pp. 818–833. Springer, 2014. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017a. URL https://arxiv.org/abs/1611.03530.<br />
<br />
Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. arXiv preprint arXiv:1707.01083, 2017b.<br />
<br />
Shuchang Zhou, Zekun Ni, Xinyu Zhou, He Wen, Yuxin Wu, and Yuheng Zou. Dorefa-net: Training low bitwidth convolutional neural networks with low bitwidth gradients. arXiv preprint arXiv:1606.06160, 2016.<br />
<br />
A. Rosenfeld and J. K. Tsotsos, “Intriguing properties of randomly weighted networks: Generalizing while learning next to nothing,” arXiv preprint arXiv:1802.00844, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fix_your_classifier:_the_marginal_value_of_training_the_last_weight_layer&diff=42214Fix your classifier: the marginal value of training the last weight layer2018-12-02T23:20:08Z<p>A22ravi: /* Introduction */ - Repeated in the previous work section</p>
<hr />
<div><br />
The code for the proposed model is available at https://github.com/eladhoffer/fix_your_classifier.<br />
<br />
=Introduction=<br />
<br />
Deep neural networks have become widely used for machine learning, achieving state-of-the-art results on many tasks. One of the most common tasks they are used for is classification. For example, convolutional neural networks (CNNs) are used to classify images to a semantic category. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more computational resources.<br />
<br />
=Brief Overview=<br />
<br />
In order to alleviate the aforementioned problem, the authors propose that the final layer of the classifier be fixed (up to a global scale constant). They argue that with little or no loss of accuracy for most classification tasks, the method provides significant memory and computational benefits. In addition, they show that by initializing the classifier with a Hadamard matrix the inference could be made faster as well.<br />
<br />
=Previous Work=<br />
<br />
Training NN models and using them for inference requires large amounts of memory and computational resources; thus, extensive amount of research has been done lately to reduce the size of networks which are as follows:<br />
<br />
* Weight sharing and specification (Han et al., 2015)<br />
<br />
* Mixed precision to reduce the size of the neural networks by half (Micikevicius et al., 2017)<br />
<br />
* Low-rank approximations to speed up CNN (Tai et al., 2015)<br />
<br />
* Quantization of weights, activations, and gradients to further reduce computation during training (Hubara et al., 2016b; Li et al., 2016 and Zhou et al., 2016). Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
<br />
Some of the past works have also put forward the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on many of the classification tasks. However, the authors' proposal in the current paper suggests the reverse proposal - common Neural Network models used can learn useful representations even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Background=<br />
<br />
A Convolutional Neural Network (CNN) is comprised of one or more convolutional layers (often with a subsampling step) and then followed by one or more fully connected layers as in a standard multilayer neural network. The architecture of a CNN is designed to take advantage of the 2D structure of an input image (or other 2D input such as a speech signal). This is achieved with local connections and tied weights followed by some form of pooling which results in translation invariant features. Another benefit of CNNs is that they are easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. <br />
<br />
A CNN consists of a number of convolutional and subsampling layers optionally followed by fully connected layers. The input to a convolutional layer is a <math>m \times m \times r</math> image where m is the height and width of the image and <math>r</math> is the number of channels, e.g. an RGB image has <math>r=3</math>. The convolutional layer will have <math>k</math> filters (or kernels) of size <math>n \times n \times q</math> where <math>n</math> is smaller than the dimension of the image and <math>q</math> can either be the same as the number of channels <math>r</math> or smaller and may vary for each kernel. The size of the filters gives rise to the locally connected structure which are each convolved with the image to produce <math>k</math> feature maps of size <math>m−n+1</math>. Each map is then subsampled typically with mean or max pooling over <math>p \times p</math> contiguous regions where <math>p</math> ranges between 2 for small images (e.g. MNIST) and is usually not more than 5 for larger inputs. Either before or after the subsampling layer an additive bias and sigmoidal nonlinearity is applied to each feature map. <br />
<br />
CNNs are commonly used to solve a variety of spatial and temporal tasks. Earlier architectures of CNNs (LeCun et al., 1998; Krizhevsky et al., 2012) used a set of fully-connected layers at later stages of the network, presumably to allow classification based on global features of an image.<br />
<br />
<br />
<br />
== Shortcomings of the Final Classification Layer and its Solution ==<br />
<br />
Zeiler & Fergus, 2014 showed that despite the enormous number of trainable parameters these layers add to the model, they are known to have a rather marginal impact on the final performance of the network.<br />
<br />
It has been shown previously that these layers could be easily compressed and reduced after a model was trained by simple means such as matrix decomposition and sparsification (Han et al., 2015). Modern architecture choices are characterized with the removal of most of the fully connected layers (Lin et al., 2013; Szegedy et al., 2015; He et al., 2016), that lead to better generalization and overall accuracy, together with a huge decrease in the number of trainable parameters. Additionally, numerous works showed that CNNs can be trained in a metric learning regime (Bromley et al., 1994; Schroff et al., 2015; Hoffer & Ailon, 2015), where no explicit classification layer was introduced and the objective regarded only distance measures between intermediate representations. Hardt & Ma (2017) suggested an all-convolutional network variant, where they kept the original initialization of the classification layer fixed with no negative impact on performance on the CIFAR-10 dataset.<br />
<br />
=Proposed Method=<br />
<br />
The aforementioned works provide evidence that fully-connected layers are in fact redundant and play a small role in learning and generalization. In this work, the authors have suggested that the parameters used for the final classification transform are completely redundant, and can be replaced with a predetermined linear transform. This holds for even in large-scale models and classification tasks, such as recent architectures trained on the ImageNet benchmark (Deng et al., 2009).<br />
<br />
==Using a Fixed Classifier==<br />
<br />
Suppose the final representation obtained by the network (the last hidden layer) is represented as <math>x = F(z;\theta)</math> where <math>F</math> is assumed to be a deep neural network with input z and parameters θ, e.g., a convolutional network, trained by backpropagation.<br />
<br />
In common NN models, this representation is followed by an additional affine transformation, <math>y = W^T x + b</math> ,where <math>W</math> and <math>b</math> are also trained by back-propagation.<br />
<br />
For input <math>x</math> of <math>N</math> length, and <math>C</math> different possible outputs, <math>W</math> is required to be a matrix of <math>N ×<br />
C</math>. Training is done using cross-entropy loss, by feeding the network outputs through a softmax activation<br />
<br />
<math><br />
v_i = \frac{e^{y_i}}{\sum_{j}^{C}{e^{y_j}}}, i &isin; </math> { <math> {1, . . . , C} </math> }<br />
<br />
and reducing the expected negative log likelihood with respect to ground-truth target <math> t &isin; </math> { <math> {1, . . . , C} </math> },<br />
by minimizing the loss function:<br />
<br />
<math><br />
L(x, t) = −\text{log}\ {v_t} = −{w_t}·{x} − b_t + \text{log} ({\sum_{j}^{C}e^{w_j . x + b_j}})<br />
</math><br />
<br />
where <math>w_i</math> is the <math>i</math>-th column of <math>W</math>.<br />
<br />
==Choosing the Projection Matrix==<br />
<br />
To evaluate the conjecture regarding the importance of the final classification transformation, the trainable parameter matrix <math>W</math> is replaced with a fixed orthonormal projection <math> Q &isin; R^{N×C} </math>, such that <math> &forall; i &ne; j : q_i · q_j = 0 </math> and <math> || q_i ||_{2} = 1 </math>, where <math>q_i</math> is the <math>i</math>th column of <math>Q</math>. This is ensured by a simple random sampling and singular-value decomposition<br />
<br />
As the rows of classifier weight matrix are fixed with an equally valued <math>L_{2}</math> norm, we find it beneficial<br />
to also restrict the representation of <math>x</math> by normalizing it to reside on the <math>n</math>-dimensional sphere:<br />
<br />
<center><math><br />
\hat{x} = \frac{x}{||x||_{2}}<br />
</math></center><br />
<br />
This allows faster training and convergence, as the network does not need to account for changes in the scale of its weights. However, it has now an issue that <math>q_i · \hat{x} </math> is bounded between −1 and 1. This causes convergence issues, as the softmax function is scale sensitive, and the network is affected by the inability to re-scale its input. This issue is amended with a fixed scale <math>T</math> applied to softmax inputs <math>f(y) = softmax(\frac{1}{T}y)</math>, also known as the ''softmax temperature''. However, this introduces an additional hyper-parameter which may differ between networks and datasets. So, the authors propose to introduce a single scalar parameter <math>\alpha</math> to learn the softmax scale, effectively functioning as an inverse of the softmax temperature <math>\frac{1}{T}</math>. The normalized weights and an additional scale coefficient are also used, specially using a single scale for all entries in the weight matrix. The additional vector of bias parameters <math>b &isin; \mathbb{R}^{C}</math> is kept the same and the model is trained using the traditional negative-log-likelihood criterion. Explicitly, the classifier output is now:<br />
<br />
<center><br />
<math><br />
v_i=\frac{e^{\alpha q_i &middot; \hat{x} + b_i}}{\sum_{j}^{C} e^{\alpha q_j &middot; \hat{x} + b_j}}, i &isin; </math> { <math> {1,...,C} </math>}<br />
</center><br />
<br />
and the loss to be minimized is:<br />
<br />
<center><math><br />
L(x, t) = -\alpha q_t &middot; \frac{x}{||x||_{2}} + b_t + \text{log} (\sum_{i=1}^{C} \text{exp}((\alpha q_i &middot; \frac{x}{||x||_{2}} + b_i)))<br />
</math></center><br />
<br />
where <math>x</math> is the final representation obtained by the network for a specific sample, and <math> t &isin; </math> { <math> {1, . . . , C} </math> } is the ground-truth label for that sample. The behaviour of the parameter <math> \alpha </math> over time, which is logarithmic in nature and has the same behavior exhibited by the norm of a learned classifier, is shown in<br />
[[Media: figure1_log_behave.png| Figure 1]].<br />
<br />
<center>[[File:figure1_log_behave.png]]</center><br />
<br />
When <math> -1 \le q_i · \hat{x} \le 1 </math>, a possible cosine angle loss is <br />
<br />
<center>[[File:caloss.png]]</center><br />
<br />
But its final validation accuracy has a slight decrease, compared to original models.<br />
<br />
==Using a Hadmard Matrix==<br />
<br />
To recall, Hadmard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are either +1 or −1.<br />
Furthermore, <math> H </math> is orthogonal, such that <math> HH^{T} = nI_n </math> where <math>I_n</math> is the identity matrix. Instead of using the entire Hadmard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all <math>C</math> rows are orthogonal as the final classification layer is such that:<br />
<br />
<center><math><br />
y = \hat{H} \hat{x} + b<br />
</math></center><br />
<br />
This usage allows two main benefits:<br />
* A deterministic, low-memory and easily generated matrix that can be used for classification.<br />
* Removal of the need to perform a full matrix-matrix multiplication - as multiplying by a Hadamard matrix can be done by simple sign manipulation and addition.<br />
<br />
Here, <math>n</math> must be a multiple of 4, but it can be easily truncated to fit normally defined networks. Also, as the classifier weights are fixed to need only 1-bit precision, it is now possible to focus our attention on the features preceding it.<br />
<br />
=Experimental Results=<br />
<br />
The authors have evaluated their proposed model on the following datasets:<br />
<br />
==CIFAR-10/100==<br />
<br />
===About the Dataset===<br />
<br />
CIFAR-10 is an image classification benchmark dataset containing 50,000 training images and 10,000 test images. The images are in color and contain 32×32 pixels. There are 10 possible classes of various animals and vehicles. CIFAR-100 holds the same number of images of the same size, but contains 100 different classes.<br />
<br />
===Training Details===<br />
<br />
The authors trained a residual network ( He et al., 2016) on the CIFAR-10 dataset. The network depth was 56 and the same hyper-parameters as in the original work were used. A comparison of the two variants, i.e., the learned classifier and the proposed classifier with a fixed transformation is shown in [[Media: figure1_resnet_cifar10.png | Figure 2]].<br />
<br />
<center>[[File: figure1_resnet_cifar10.png]]</center><br />
<br />
These results demonstrate that although the training error is considerably lower for the network with learned classifier, both models achieve the same classification accuracy on the validation set. The authors' conjecture is that with the new fixed parameterization, the network can no longer increase the norm of a given sample’s representation - thus learning its label requires more effort. As this may happen for specific seen samples - it affects only training error.<br />
<br />
The authors also compared using a fixed scale variable <math>\alpha </math> at different values vs. the learned parameter. Results for <math> \alpha = </math> {0.1, 1, 10} are depicted in [[Media: figure3_alpha_resnet_cifar.png| Figure 3]] for both training and validation error and as can be seen, similar validation accuracy can be obtained using a fixed scale value (in this case <math>\alpha </math>= 1 or 10 will suffice) at the expense of another hyper-parameter to seek. In all the further experiments the scaling parameter <math> \alpha </math> was regularized with the same weight decay coefficient used on original classifier. Although learning the scale is not necessary, but it will help convergence during training.<br />
<br />
<center>[[File: figure3_alpha_resnet_cifar.png]]</center><br />
<br />
The authors then train the model on CIFAR-100 dataset. They used the DenseNet-BC model from Huang et al. (2017) with a depth of 100 layers and k = 12. The higher number of classes caused the number of parameters to grow and encompassed about 4% of the whole model. However, validation accuracy for the fixed-classifier model remained equally good as the original model, and the same training curve was observed as earlier.<br />
<br />
==IMAGENET==<br />
<br />
===About the Dataset===<br />
<br />
The Imagenet dataset introduced by Deng et al. (2009) spans over 1000 visual classes, and over 1.2 million samples. This is supposedly a more challenging dataset to work on as compared to CIFAR-10/100.<br />
<br />
===Experiment Details===<br />
<br />
The authors evaluated their fixed classifier method on Imagenet using Resnet50 by He et al. (2016) and Densenet169 model (Huang et al., 2017) as described in the original work. Using a fixed classifier removed approximately 2-million parameters were from the model, accounting for about 8% and 12 % of the model parameters respectively. The experiments revealed similar trends as observed on CIFAR-10.<br />
<br />
For a more stricter evaluation, the authors also trained a Shufflenet architecture (Zhang et al., 2017b), which was designed to be used in low memory and limited computing platforms and has parameters making up the majority of the model. They were able to reduce the parameters to 0.86 million as compared to 0.96 million parameters in the final layer of the original model. Again, the proposed modification in the original model gave similar convergence results on validation accuracy. Interestingly, this method allowed Imagenet training in an under-specified regime, where there are<br />
more training samples than the number of parameters. This is an unconventional regime for modern deep networks, which are usually over-specified to have many more parameters than training samples (Zhang et al., 2017a).<br />
<br />
The overall results of the fixed-classifier are summarized in [[Media: table1_fixed_results.png | Table 1]].<br />
<br />
<center>[[File: table1_fixed_results.png]]</center><br />
<br />
==Language Modelling==<br />
<br />
Recent works have empirically found that using the same weights for both word embedding and classifier can yield equal or better results than using a separate pair of weights. So the authors experimented with fix-classifiers on language modeling as it also requires classification of all possible tokens available in the task vocabulary. They trained a recurrent model with 2-layers of LSTM (Hochreiter & Schmidhuber, 1997) and embedding + hidden size of 512 on the WikiText2 dataset (Merity et al., 2016), using same settings as in Merity et al. (2017). WikiText2 dataset contains about 33K different words, so the number of parameters expected in the embedding and classifier layer was about 34-million. This number is about 89% of the total number of parameters used for the whole model which is 38-million. However, using a random orthogonal transform yielded poor results compared to learned embedding. This was suspected to be due to semantic relationships captured in the embedding layer of language models, which is not the case in image classification task. The intuition was further confirmed by the much better results when pre-trained embeddings using word2vec algorithm by Mikolov et al. (2013) or PMI factorization as suggested by Levy & Goldberg (2014), were used. The final result used 89% fewer parameters than a fully learned model, with only marginally worse perplexity. The authors posit that this implies a required structure in word embedding that originates from the semantic relatedness between words, and unbalanced classes. They further suggest that with more efficient ways to train word embeddings, it may be possible to mitigate the issues arising from this structure and class imbalance. <br />
<br />
<center>[[File: language.png]]</center><br />
<br />
=Discussion=<br />
<br />
==Implications and Use Cases==<br />
<br />
With the increasing number of classes in the benchmark datasets, computational demands for the final classifier will increase as well. In order to understand the problem better, the authors observe the work by Sun et al. (2017), which introduced JFT-300M - an internal Google dataset with over 18K different classes. Using a Resnet50 (He et al., 2016), with a 2048 sized representation led to a model with over 36M parameters meaning that over 60% of the model parameters resided in the final classification layer. Sun et al. (2017) also describe the difficulty in distributing so many parameters over the training servers involving a non-trivial overhead during synchronization of the model for update. The authors claim that the fixed-classifier would help considerably in this kind of scenario - where using a fixed classifier removes the need to do any gradient synchronization for the final layer. Furthermore, introduction of Hadamard matrix removes the need to save the transformation altogether, thereby, making it more efficient and allowing considerable memory and computational savings.<br />
<br />
==Possible Caveats==<br />
<br />
The good performance of fixed-classifiers relies on the ability of the preceding layers to learn separable representations. This could be affected when the ratio between learned features and number of classes is small – that is, when <math> C > N</math>. However, they tested their method in such cases and their model performed well and provided good results.<br />
Another factor that can affect the performance of their model using a fixed classifier is when the classes are highly correlated. In that case, the fixed classifier actually cannot support correlated classes and thus, the network could have some difficulty to learn. For a language model, word classes tend to have highly correlated instances, which also lead to difficult learning process.<br />
<br />
Also, this proposed approach will only eliminate the computation of the classifier weights, so when the classes are fewer, the computation saving effect will not be readily apparent.<br />
<br />
==Future Work==<br />
<br />
<br />
The use of fixed classifiers might be further simplified in Binarized Neural Networks (Hubara et al., 2016a), where the activations and weights are restricted to ±1 during propagations. In that case, the norm of the last hidden layer would be constant for all samples (equal to the square root of the hidden layer width). The constant could then be absorbed into the scale constant <math>\alpha</math>, and there is no need in a per-sample normalization.<br />
<br />
Additionally, more efficient ways to learn a word embedding should also be explored where similar redundancy in classifier weights may suggest simpler forms of token representations - such as low-rank or sparse versions.<br />
<br />
A related paper was published that claims that fixing most of the parameters of the neural network achieves comparable results with learning all of them [A. Rosenfeld and J. K. Tsotsos]<br />
<br />
=Conclusion=<br />
<br />
In this work, the authors argue that the final classification layer in deep neural networks is redundant and suggest removing the parameters from the classification layer. The empirical results from experiments on the CIFAR and IMAGENET datasets suggest that such a change lead to little or almost no decline in the performance of the architecture. Furthermore, using a Hadmard matrix as classifier might lead to some computational benefits when properly implemented, and save memory otherwise spent on large amount of transformation coefficients.<br />
<br />
Another possible scope of research that could be pointed out for future could be to find new efficient methods to create pre-defined word embeddings, which require huge amount of parameters that can possibly be avoided when learning a new task. Therefore, more emphasis should be given to the representations learned by the non-linear parts of the neural networks - up to the final classifier, as it seems highly redundant.<br />
<br />
=Critique=<br />
<br />
The paper proposes an interesting idea that has a potential use case when designing memory-efficient neural networks. The experiments shown in the paper are quite rigorous and provide support to the authors' claim. However, it would have been more helpful if the authors had described a bit more about efficient implementation of the Hadamard matrix and how to scale this method for larger datasets (cases with <math> C >N</math>).<br />
<br />
Moreover, one of the main intuitions of the paper has introduced to be computational cost but it has left out to compare a fixed and learned classifier based on the computational cost and then investigate whether it worth the drop in performance or not considering the fact that not always the output can be degraded because of need for speed! At least a discussion on this issue is expected.<br />
<br />
On the other hand, the computational cost and performance change after fixation of classifier could be related to dataset and the nature and complexity of it. Mostly, having 1000 classes makes the classification more crucial than 2 classes. An evaluation of this topic is also needed.<br />
<br />
Another interesting experiment to do would be to look this technique interacts with distillation when used in the teacher or student network or both. For instance, Does fixing the features make it more difficult to place dog than on boat when classifying a cat? Do networks with fixed classifier weights make worse teachers for distillation?<br />
<br />
=References=<br />
<br />
Madhu S Advani and Andrew M Saxe. High-dimensional dynamics of generalization error in neural networks. arXiv preprint arXiv:1710.03667, 2017.<br />
<br />
Peter Bartlett, Dylan J Foster, and Matus Telgarsky. Spectrally-normalized margin bounds for neural networks. arXiv preprint arXiv:1706.08498, 2017.<br />
<br />
Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Sackinger, and Roopak Shah. Signature verification using a” siamese” time delay neural network. In Advances in Neural Information Processing Systems, pp. 737–744, 1994.<br />
<br />
Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Binaryconnect: Training deep neural networks with binary weights during propagations. In Advances in Neural Information Processing Systems, pp. 3123–3131, 2015.<br />
<br />
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 248–255. IEEE, 2009.<br />
<br />
Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro. Implicit regularization in matrix factorization. arXiv preprint arXiv:1705.09280, 2017.<br />
<br />
Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.<br />
<br />
Moritz Hardt and Tengyu Ma. Identity matters in deep learning. 2017.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.<br />
<br />
A Hedayat, WD Wallis, et al. Hadamard matrices and their applications. The Annals of Statistics, 6<br />
(6):1184–1238, 1978.<br />
<br />
Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.<br />
<br />
Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International Workshop on Similarity-Based Pattern Recognition, pp. 84–92. Springer, 2015.<br />
<br />
Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. 2017.<br />
<br />
Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017.<br />
<br />
Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017.<br />
<br />
Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew. Extreme learning machine: theory and applications. Neurocomputing, 70(1):489–501, 2006.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. In Advances in Neural Information Processing Systems 29 (NIPS’16), 2016a.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Quantized neural networks: Training neural networks with low precision weights and activations. arXiv preprint arXiv:1609.07061, 2016b.<br />
<br />
Hakan Inan, Khashayar Khosravi, and Richard Socher. Tying word vectors and word classifiers: A loss framework for language modeling. arXiv preprint arXiv:1611.01462, 2016.<br />
<br />
Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. arXiv preprint arXiv:1405.3866, 2014.<br />
<br />
Alex Krizhevsky. Learning multiple layers of features from tiny images. 2009.<br />
<br />
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012.<br />
<br />
Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278 2324, 1998.<br />
<br />
Omer Levy and Yoav Goldberg. Neural word embedding as implicit matrix factorization. In Advances in neural information processing systems, pp. 2177–2185, 2014.<br />
<br />
Fengfu Li, Bo Zhang, and Bin Liu. Ternary weight networks. arXiv preprint arXiv:1605.04711, 2016.<br />
<br />
Min Lin, Qiang Chen, and Shuicheng Yan. Network in network. arXiv preprint arXiv:1312.4400, 2013.<br />
<br />
Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. arXiv preprint arXiv:1609.07843, 2016.<br />
<br />
Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017.<br />
<br />
Paulius Micikevicius, Sharan Narang, Jonah Alben, Gregory Diamos, Erich Elsen, David Garcia, Boris Ginsburg, Michael Houston, Oleksii Kuchaev, Ganesh Venkatesh, et al. Mixed precision training. arXiv preprint arXiv:1710.03740, 2017.<br />
<br />
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed tations of words and phrases and their compositionality. In Advances in neural information processing systems, pp. 3111–3119, 2013.<br />
<br />
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring generalization in deep learning. arXiv preprint arXiv:1706.08947, 2017.<br />
Jooyoung Park and Irwin W Sandberg. Universal approximation using radial-basis-function networks. Neural computation, 3(2):246–257, 1991.<br />
<br />
Ofir Press and Lior Wolf. Using the output embedding to improve language models. EACL 2017,<br />
pp. 157, 2017.<br />
<br />
Itay Safran and Ohad Shamir. On the quality of the initial basin in overspecified neural networks. In International Conference on Machine Learning, pp. 774–782, 2016.<br />
<br />
Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016.<br />
<br />
Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 815–823, 2015.<br />
<br />
Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. arXiv preprint arXiv:1707.04926, 2017.<br />
<br />
Daniel Soudry and Yair Carmon. No bad local minima: Data independent training error guarantees for multilayer neural networks. arXiv preprint arXiv:1605.08361, 2016.<br />
<br />
Daniel Soudry and Elad Hoffer. Exponentially vanishing sub-optimal local minima in multilayer neural networks. arXiv preprint arXiv:1702.05777, 2017.<br />
<br />
Daniel Soudry, Elad Hoffer, and Nathan Srebro. The implicit bias of gradient descent on separable data. 2018.<br />
<br />
Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.<br />
<br />
Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. arXiv preprint arXiv:1707.02968, 2017.<br />
<br />
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1–9, 2015.<br />
<br />
Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2818–2826, 2016.<br />
<br />
Cheng Tai, Tong Xiao, Yi Zhang, Xiaogang Wang, et al. Convolutional neural networks with lowrank regularization. arXiv preprint arXiv:1511.06067, 2015.<br />
<br />
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2017.<br />
Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
Bo Xie, Yingyu Liang, and Le Song. Diversity leads to generalization in neural networks. arXiv preprint arXiv:1611.03131, 2016.<br />
<br />
Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European conference on computer vision, pp. 818–833. Springer, 2014. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017a. URL https://arxiv.org/abs/1611.03530.<br />
<br />
Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. arXiv preprint arXiv:1707.01083, 2017b.<br />
<br />
Shuchang Zhou, Zekun Ni, Xinyu Zhou, He Wen, Yuxin Wu, and Yuheng Zou. Dorefa-net: Training low bitwidth convolutional neural networks with low bitwidth gradients. arXiv preprint arXiv:1606.06160, 2016.<br />
<br />
A. Rosenfeld and J. K. Tsotsos, “Intriguing properties of randomly weighted networks: Generalizing while learning next to nothing,” arXiv preprint arXiv:1802.00844, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fix_your_classifier:_the_marginal_value_of_training_the_last_weight_layer&diff=42213Fix your classifier: the marginal value of training the last weight layer2018-12-02T23:19:36Z<p>A22ravi: /* Previous Work */</p>
<hr />
<div><br />
The code for the proposed model is available at https://github.com/eladhoffer/fix_your_classifier.<br />
<br />
=Introduction=<br />
<br />
Deep neural networks have become widely used for machine learning, achieving state-of-the-art results on many tasks. One of the most common tasks they are used for is classification. For example, convolutional neural networks (CNNs) are used to classify images to a semantic category. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more computational resources. Thus, extensive amount of research has been done lately to reduce the size of networks. Han et al. (2015) used weight sharing and specification, Micikevicius et al. (2017) used mixed precision to reduce the size of the neural networks by half. Tai et al. (2015) and Jaderberg et al. (2014) used low rank approximations to speed up NNs. Hubara et al. (2016b), Li et al. (2016) and Zhou et al. (2016), used a more aggressive approach, in which weights, activations and gradients were quantized to further reduce computation during training. Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
Past work noted the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on several tasks. This study suggests the reverse proposal - that common NN models used can learn useful representation even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Brief Overview=<br />
<br />
In order to alleviate the aforementioned problem, the authors propose that the final layer of the classifier be fixed (up to a global scale constant). They argue that with little or no loss of accuracy for most classification tasks, the method provides significant memory and computational benefits. In addition, they show that by initializing the classifier with a Hadamard matrix the inference could be made faster as well.<br />
<br />
=Previous Work=<br />
<br />
Training NN models and using them for inference requires large amounts of memory and computational resources; thus, extensive amount of research has been done lately to reduce the size of networks which are as follows:<br />
<br />
* Weight sharing and specification (Han et al., 2015)<br />
<br />
* Mixed precision to reduce the size of the neural networks by half (Micikevicius et al., 2017)<br />
<br />
* Low-rank approximations to speed up CNN (Tai et al., 2015)<br />
<br />
* Quantization of weights, activations, and gradients to further reduce computation during training (Hubara et al., 2016b; Li et al., 2016 and Zhou et al., 2016). Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
<br />
Some of the past works have also put forward the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on many of the classification tasks. However, the authors' proposal in the current paper suggests the reverse proposal - common Neural Network models used can learn useful representations even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Background=<br />
<br />
A Convolutional Neural Network (CNN) is comprised of one or more convolutional layers (often with a subsampling step) and then followed by one or more fully connected layers as in a standard multilayer neural network. The architecture of a CNN is designed to take advantage of the 2D structure of an input image (or other 2D input such as a speech signal). This is achieved with local connections and tied weights followed by some form of pooling which results in translation invariant features. Another benefit of CNNs is that they are easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. <br />
<br />
A CNN consists of a number of convolutional and subsampling layers optionally followed by fully connected layers. The input to a convolutional layer is a <math>m \times m \times r</math> image where m is the height and width of the image and <math>r</math> is the number of channels, e.g. an RGB image has <math>r=3</math>. The convolutional layer will have <math>k</math> filters (or kernels) of size <math>n \times n \times q</math> where <math>n</math> is smaller than the dimension of the image and <math>q</math> can either be the same as the number of channels <math>r</math> or smaller and may vary for each kernel. The size of the filters gives rise to the locally connected structure which are each convolved with the image to produce <math>k</math> feature maps of size <math>m−n+1</math>. Each map is then subsampled typically with mean or max pooling over <math>p \times p</math> contiguous regions where <math>p</math> ranges between 2 for small images (e.g. MNIST) and is usually not more than 5 for larger inputs. Either before or after the subsampling layer an additive bias and sigmoidal nonlinearity is applied to each feature map. <br />
<br />
CNNs are commonly used to solve a variety of spatial and temporal tasks. Earlier architectures of CNNs (LeCun et al., 1998; Krizhevsky et al., 2012) used a set of fully-connected layers at later stages of the network, presumably to allow classification based on global features of an image.<br />
<br />
<br />
<br />
== Shortcomings of the Final Classification Layer and its Solution ==<br />
<br />
Zeiler & Fergus, 2014 showed that despite the enormous number of trainable parameters these layers add to the model, they are known to have a rather marginal impact on the final performance of the network.<br />
<br />
It has been shown previously that these layers could be easily compressed and reduced after a model was trained by simple means such as matrix decomposition and sparsification (Han et al., 2015). Modern architecture choices are characterized with the removal of most of the fully connected layers (Lin et al., 2013; Szegedy et al., 2015; He et al., 2016), that lead to better generalization and overall accuracy, together with a huge decrease in the number of trainable parameters. Additionally, numerous works showed that CNNs can be trained in a metric learning regime (Bromley et al., 1994; Schroff et al., 2015; Hoffer & Ailon, 2015), where no explicit classification layer was introduced and the objective regarded only distance measures between intermediate representations. Hardt & Ma (2017) suggested an all-convolutional network variant, where they kept the original initialization of the classification layer fixed with no negative impact on performance on the CIFAR-10 dataset.<br />
<br />
=Proposed Method=<br />
<br />
The aforementioned works provide evidence that fully-connected layers are in fact redundant and play a small role in learning and generalization. In this work, the authors have suggested that the parameters used for the final classification transform are completely redundant, and can be replaced with a predetermined linear transform. This holds for even in large-scale models and classification tasks, such as recent architectures trained on the ImageNet benchmark (Deng et al., 2009).<br />
<br />
==Using a Fixed Classifier==<br />
<br />
Suppose the final representation obtained by the network (the last hidden layer) is represented as <math>x = F(z;\theta)</math> where <math>F</math> is assumed to be a deep neural network with input z and parameters θ, e.g., a convolutional network, trained by backpropagation.<br />
<br />
In common NN models, this representation is followed by an additional affine transformation, <math>y = W^T x + b</math> ,where <math>W</math> and <math>b</math> are also trained by back-propagation.<br />
<br />
For input <math>x</math> of <math>N</math> length, and <math>C</math> different possible outputs, <math>W</math> is required to be a matrix of <math>N ×<br />
C</math>. Training is done using cross-entropy loss, by feeding the network outputs through a softmax activation<br />
<br />
<math><br />
v_i = \frac{e^{y_i}}{\sum_{j}^{C}{e^{y_j}}}, i &isin; </math> { <math> {1, . . . , C} </math> }<br />
<br />
and reducing the expected negative log likelihood with respect to ground-truth target <math> t &isin; </math> { <math> {1, . . . , C} </math> },<br />
by minimizing the loss function:<br />
<br />
<math><br />
L(x, t) = −\text{log}\ {v_t} = −{w_t}·{x} − b_t + \text{log} ({\sum_{j}^{C}e^{w_j . x + b_j}})<br />
</math><br />
<br />
where <math>w_i</math> is the <math>i</math>-th column of <math>W</math>.<br />
<br />
==Choosing the Projection Matrix==<br />
<br />
To evaluate the conjecture regarding the importance of the final classification transformation, the trainable parameter matrix <math>W</math> is replaced with a fixed orthonormal projection <math> Q &isin; R^{N×C} </math>, such that <math> &forall; i &ne; j : q_i · q_j = 0 </math> and <math> || q_i ||_{2} = 1 </math>, where <math>q_i</math> is the <math>i</math>th column of <math>Q</math>. This is ensured by a simple random sampling and singular-value decomposition<br />
<br />
As the rows of classifier weight matrix are fixed with an equally valued <math>L_{2}</math> norm, we find it beneficial<br />
to also restrict the representation of <math>x</math> by normalizing it to reside on the <math>n</math>-dimensional sphere:<br />
<br />
<center><math><br />
\hat{x} = \frac{x}{||x||_{2}}<br />
</math></center><br />
<br />
This allows faster training and convergence, as the network does not need to account for changes in the scale of its weights. However, it has now an issue that <math>q_i · \hat{x} </math> is bounded between −1 and 1. This causes convergence issues, as the softmax function is scale sensitive, and the network is affected by the inability to re-scale its input. This issue is amended with a fixed scale <math>T</math> applied to softmax inputs <math>f(y) = softmax(\frac{1}{T}y)</math>, also known as the ''softmax temperature''. However, this introduces an additional hyper-parameter which may differ between networks and datasets. So, the authors propose to introduce a single scalar parameter <math>\alpha</math> to learn the softmax scale, effectively functioning as an inverse of the softmax temperature <math>\frac{1}{T}</math>. The normalized weights and an additional scale coefficient are also used, specially using a single scale for all entries in the weight matrix. The additional vector of bias parameters <math>b &isin; \mathbb{R}^{C}</math> is kept the same and the model is trained using the traditional negative-log-likelihood criterion. Explicitly, the classifier output is now:<br />
<br />
<center><br />
<math><br />
v_i=\frac{e^{\alpha q_i &middot; \hat{x} + b_i}}{\sum_{j}^{C} e^{\alpha q_j &middot; \hat{x} + b_j}}, i &isin; </math> { <math> {1,...,C} </math>}<br />
</center><br />
<br />
and the loss to be minimized is:<br />
<br />
<center><math><br />
L(x, t) = -\alpha q_t &middot; \frac{x}{||x||_{2}} + b_t + \text{log} (\sum_{i=1}^{C} \text{exp}((\alpha q_i &middot; \frac{x}{||x||_{2}} + b_i)))<br />
</math></center><br />
<br />
where <math>x</math> is the final representation obtained by the network for a specific sample, and <math> t &isin; </math> { <math> {1, . . . , C} </math> } is the ground-truth label for that sample. The behaviour of the parameter <math> \alpha </math> over time, which is logarithmic in nature and has the same behavior exhibited by the norm of a learned classifier, is shown in<br />
[[Media: figure1_log_behave.png| Figure 1]].<br />
<br />
<center>[[File:figure1_log_behave.png]]</center><br />
<br />
When <math> -1 \le q_i · \hat{x} \le 1 </math>, a possible cosine angle loss is <br />
<br />
<center>[[File:caloss.png]]</center><br />
<br />
But its final validation accuracy has a slight decrease, compared to original models.<br />
<br />
==Using a Hadmard Matrix==<br />
<br />
To recall, Hadmard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are either +1 or −1.<br />
Furthermore, <math> H </math> is orthogonal, such that <math> HH^{T} = nI_n </math> where <math>I_n</math> is the identity matrix. Instead of using the entire Hadmard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all <math>C</math> rows are orthogonal as the final classification layer is such that:<br />
<br />
<center><math><br />
y = \hat{H} \hat{x} + b<br />
</math></center><br />
<br />
This usage allows two main benefits:<br />
* A deterministic, low-memory and easily generated matrix that can be used for classification.<br />
* Removal of the need to perform a full matrix-matrix multiplication - as multiplying by a Hadamard matrix can be done by simple sign manipulation and addition.<br />
<br />
Here, <math>n</math> must be a multiple of 4, but it can be easily truncated to fit normally defined networks. Also, as the classifier weights are fixed to need only 1-bit precision, it is now possible to focus our attention on the features preceding it.<br />
<br />
=Experimental Results=<br />
<br />
The authors have evaluated their proposed model on the following datasets:<br />
<br />
==CIFAR-10/100==<br />
<br />
===About the Dataset===<br />
<br />
CIFAR-10 is an image classification benchmark dataset containing 50,000 training images and 10,000 test images. The images are in color and contain 32×32 pixels. There are 10 possible classes of various animals and vehicles. CIFAR-100 holds the same number of images of the same size, but contains 100 different classes.<br />
<br />
===Training Details===<br />
<br />
The authors trained a residual network ( He et al., 2016) on the CIFAR-10 dataset. The network depth was 56 and the same hyper-parameters as in the original work were used. A comparison of the two variants, i.e., the learned classifier and the proposed classifier with a fixed transformation is shown in [[Media: figure1_resnet_cifar10.png | Figure 2]].<br />
<br />
<center>[[File: figure1_resnet_cifar10.png]]</center><br />
<br />
These results demonstrate that although the training error is considerably lower for the network with learned classifier, both models achieve the same classification accuracy on the validation set. The authors' conjecture is that with the new fixed parameterization, the network can no longer increase the norm of a given sample’s representation - thus learning its label requires more effort. As this may happen for specific seen samples - it affects only training error.<br />
<br />
The authors also compared using a fixed scale variable <math>\alpha </math> at different values vs. the learned parameter. Results for <math> \alpha = </math> {0.1, 1, 10} are depicted in [[Media: figure3_alpha_resnet_cifar.png| Figure 3]] for both training and validation error and as can be seen, similar validation accuracy can be obtained using a fixed scale value (in this case <math>\alpha </math>= 1 or 10 will suffice) at the expense of another hyper-parameter to seek. In all the further experiments the scaling parameter <math> \alpha </math> was regularized with the same weight decay coefficient used on original classifier. Although learning the scale is not necessary, but it will help convergence during training.<br />
<br />
<center>[[File: figure3_alpha_resnet_cifar.png]]</center><br />
<br />
The authors then train the model on CIFAR-100 dataset. They used the DenseNet-BC model from Huang et al. (2017) with a depth of 100 layers and k = 12. The higher number of classes caused the number of parameters to grow and encompassed about 4% of the whole model. However, validation accuracy for the fixed-classifier model remained equally good as the original model, and the same training curve was observed as earlier.<br />
<br />
==IMAGENET==<br />
<br />
===About the Dataset===<br />
<br />
The Imagenet dataset introduced by Deng et al. (2009) spans over 1000 visual classes, and over 1.2 million samples. This is supposedly a more challenging dataset to work on as compared to CIFAR-10/100.<br />
<br />
===Experiment Details===<br />
<br />
The authors evaluated their fixed classifier method on Imagenet using Resnet50 by He et al. (2016) and Densenet169 model (Huang et al., 2017) as described in the original work. Using a fixed classifier removed approximately 2-million parameters were from the model, accounting for about 8% and 12 % of the model parameters respectively. The experiments revealed similar trends as observed on CIFAR-10.<br />
<br />
For a more stricter evaluation, the authors also trained a Shufflenet architecture (Zhang et al., 2017b), which was designed to be used in low memory and limited computing platforms and has parameters making up the majority of the model. They were able to reduce the parameters to 0.86 million as compared to 0.96 million parameters in the final layer of the original model. Again, the proposed modification in the original model gave similar convergence results on validation accuracy. Interestingly, this method allowed Imagenet training in an under-specified regime, where there are<br />
more training samples than the number of parameters. This is an unconventional regime for modern deep networks, which are usually over-specified to have many more parameters than training samples (Zhang et al., 2017a).<br />
<br />
The overall results of the fixed-classifier are summarized in [[Media: table1_fixed_results.png | Table 1]].<br />
<br />
<center>[[File: table1_fixed_results.png]]</center><br />
<br />
==Language Modelling==<br />
<br />
Recent works have empirically found that using the same weights for both word embedding and classifier can yield equal or better results than using a separate pair of weights. So the authors experimented with fix-classifiers on language modeling as it also requires classification of all possible tokens available in the task vocabulary. They trained a recurrent model with 2-layers of LSTM (Hochreiter & Schmidhuber, 1997) and embedding + hidden size of 512 on the WikiText2 dataset (Merity et al., 2016), using same settings as in Merity et al. (2017). WikiText2 dataset contains about 33K different words, so the number of parameters expected in the embedding and classifier layer was about 34-million. This number is about 89% of the total number of parameters used for the whole model which is 38-million. However, using a random orthogonal transform yielded poor results compared to learned embedding. This was suspected to be due to semantic relationships captured in the embedding layer of language models, which is not the case in image classification task. The intuition was further confirmed by the much better results when pre-trained embeddings using word2vec algorithm by Mikolov et al. (2013) or PMI factorization as suggested by Levy & Goldberg (2014), were used. The final result used 89% fewer parameters than a fully learned model, with only marginally worse perplexity. The authors posit that this implies a required structure in word embedding that originates from the semantic relatedness between words, and unbalanced classes. They further suggest that with more efficient ways to train word embeddings, it may be possible to mitigate the issues arising from this structure and class imbalance. <br />
<br />
<center>[[File: language.png]]</center><br />
<br />
=Discussion=<br />
<br />
==Implications and Use Cases==<br />
<br />
With the increasing number of classes in the benchmark datasets, computational demands for the final classifier will increase as well. In order to understand the problem better, the authors observe the work by Sun et al. (2017), which introduced JFT-300M - an internal Google dataset with over 18K different classes. Using a Resnet50 (He et al., 2016), with a 2048 sized representation led to a model with over 36M parameters meaning that over 60% of the model parameters resided in the final classification layer. Sun et al. (2017) also describe the difficulty in distributing so many parameters over the training servers involving a non-trivial overhead during synchronization of the model for update. The authors claim that the fixed-classifier would help considerably in this kind of scenario - where using a fixed classifier removes the need to do any gradient synchronization for the final layer. Furthermore, introduction of Hadamard matrix removes the need to save the transformation altogether, thereby, making it more efficient and allowing considerable memory and computational savings.<br />
<br />
==Possible Caveats==<br />
<br />
The good performance of fixed-classifiers relies on the ability of the preceding layers to learn separable representations. This could be affected when the ratio between learned features and number of classes is small – that is, when <math> C > N</math>. However, they tested their method in such cases and their model performed well and provided good results.<br />
Another factor that can affect the performance of their model using a fixed classifier is when the classes are highly correlated. In that case, the fixed classifier actually cannot support correlated classes and thus, the network could have some difficulty to learn. For a language model, word classes tend to have highly correlated instances, which also lead to difficult learning process.<br />
<br />
Also, this proposed approach will only eliminate the computation of the classifier weights, so when the classes are fewer, the computation saving effect will not be readily apparent.<br />
<br />
==Future Work==<br />
<br />
<br />
The use of fixed classifiers might be further simplified in Binarized Neural Networks (Hubara et al., 2016a), where the activations and weights are restricted to ±1 during propagations. In that case, the norm of the last hidden layer would be constant for all samples (equal to the square root of the hidden layer width). The constant could then be absorbed into the scale constant <math>\alpha</math>, and there is no need in a per-sample normalization.<br />
<br />
Additionally, more efficient ways to learn a word embedding should also be explored where similar redundancy in classifier weights may suggest simpler forms of token representations - such as low-rank or sparse versions.<br />
<br />
A related paper was published that claims that fixing most of the parameters of the neural network achieves comparable results with learning all of them [A. Rosenfeld and J. K. Tsotsos]<br />
<br />
=Conclusion=<br />
<br />
In this work, the authors argue that the final classification layer in deep neural networks is redundant and suggest removing the parameters from the classification layer. The empirical results from experiments on the CIFAR and IMAGENET datasets suggest that such a change lead to little or almost no decline in the performance of the architecture. Furthermore, using a Hadmard matrix as classifier might lead to some computational benefits when properly implemented, and save memory otherwise spent on large amount of transformation coefficients.<br />
<br />
Another possible scope of research that could be pointed out for future could be to find new efficient methods to create pre-defined word embeddings, which require huge amount of parameters that can possibly be avoided when learning a new task. Therefore, more emphasis should be given to the representations learned by the non-linear parts of the neural networks - up to the final classifier, as it seems highly redundant.<br />
<br />
=Critique=<br />
<br />
The paper proposes an interesting idea that has a potential use case when designing memory-efficient neural networks. The experiments shown in the paper are quite rigorous and provide support to the authors' claim. However, it would have been more helpful if the authors had described a bit more about efficient implementation of the Hadamard matrix and how to scale this method for larger datasets (cases with <math> C >N</math>).<br />
<br />
Moreover, one of the main intuitions of the paper has introduced to be computational cost but it has left out to compare a fixed and learned classifier based on the computational cost and then investigate whether it worth the drop in performance or not considering the fact that not always the output can be degraded because of need for speed! At least a discussion on this issue is expected.<br />
<br />
On the other hand, the computational cost and performance change after fixation of classifier could be related to dataset and the nature and complexity of it. Mostly, having 1000 classes makes the classification more crucial than 2 classes. An evaluation of this topic is also needed.<br />
<br />
Another interesting experiment to do would be to look this technique interacts with distillation when used in the teacher or student network or both. For instance, Does fixing the features make it more difficult to place dog than on boat when classifying a cat? Do networks with fixed classifier weights make worse teachers for distillation?<br />
<br />
=References=<br />
<br />
Madhu S Advani and Andrew M Saxe. High-dimensional dynamics of generalization error in neural networks. arXiv preprint arXiv:1710.03667, 2017.<br />
<br />
Peter Bartlett, Dylan J Foster, and Matus Telgarsky. Spectrally-normalized margin bounds for neural networks. arXiv preprint arXiv:1706.08498, 2017.<br />
<br />
Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Sackinger, and Roopak Shah. Signature verification using a” siamese” time delay neural network. In Advances in Neural Information Processing Systems, pp. 737–744, 1994.<br />
<br />
Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Binaryconnect: Training deep neural networks with binary weights during propagations. In Advances in Neural Information Processing Systems, pp. 3123–3131, 2015.<br />
<br />
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 248–255. IEEE, 2009.<br />
<br />
Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro. Implicit regularization in matrix factorization. arXiv preprint arXiv:1705.09280, 2017.<br />
<br />
Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.<br />
<br />
Moritz Hardt and Tengyu Ma. Identity matters in deep learning. 2017.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.<br />
<br />
A Hedayat, WD Wallis, et al. Hadamard matrices and their applications. The Annals of Statistics, 6<br />
(6):1184–1238, 1978.<br />
<br />
Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.<br />
<br />
Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International Workshop on Similarity-Based Pattern Recognition, pp. 84–92. Springer, 2015.<br />
<br />
Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. 2017.<br />
<br />
Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017.<br />
<br />
Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017.<br />
<br />
Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew. Extreme learning machine: theory and applications. Neurocomputing, 70(1):489–501, 2006.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. In Advances in Neural Information Processing Systems 29 (NIPS’16), 2016a.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Quantized neural networks: Training neural networks with low precision weights and activations. arXiv preprint arXiv:1609.07061, 2016b.<br />
<br />
Hakan Inan, Khashayar Khosravi, and Richard Socher. Tying word vectors and word classifiers: A loss framework for language modeling. arXiv preprint arXiv:1611.01462, 2016.<br />
<br />
Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. arXiv preprint arXiv:1405.3866, 2014.<br />
<br />
Alex Krizhevsky. Learning multiple layers of features from tiny images. 2009.<br />
<br />
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012.<br />
<br />
Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278 2324, 1998.<br />
<br />
Omer Levy and Yoav Goldberg. Neural word embedding as implicit matrix factorization. In Advances in neural information processing systems, pp. 2177–2185, 2014.<br />
<br />
Fengfu Li, Bo Zhang, and Bin Liu. Ternary weight networks. arXiv preprint arXiv:1605.04711, 2016.<br />
<br />
Min Lin, Qiang Chen, and Shuicheng Yan. Network in network. arXiv preprint arXiv:1312.4400, 2013.<br />
<br />
Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. arXiv preprint arXiv:1609.07843, 2016.<br />
<br />
Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017.<br />
<br />
Paulius Micikevicius, Sharan Narang, Jonah Alben, Gregory Diamos, Erich Elsen, David Garcia, Boris Ginsburg, Michael Houston, Oleksii Kuchaev, Ganesh Venkatesh, et al. Mixed precision training. arXiv preprint arXiv:1710.03740, 2017.<br />
<br />
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed tations of words and phrases and their compositionality. In Advances in neural information processing systems, pp. 3111–3119, 2013.<br />
<br />
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring generalization in deep learning. arXiv preprint arXiv:1706.08947, 2017.<br />
Jooyoung Park and Irwin W Sandberg. Universal approximation using radial-basis-function networks. Neural computation, 3(2):246–257, 1991.<br />
<br />
Ofir Press and Lior Wolf. Using the output embedding to improve language models. EACL 2017,<br />
pp. 157, 2017.<br />
<br />
Itay Safran and Ohad Shamir. On the quality of the initial basin in overspecified neural networks. In International Conference on Machine Learning, pp. 774–782, 2016.<br />
<br />
Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016.<br />
<br />
Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 815–823, 2015.<br />
<br />
Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. arXiv preprint arXiv:1707.04926, 2017.<br />
<br />
Daniel Soudry and Yair Carmon. No bad local minima: Data independent training error guarantees for multilayer neural networks. arXiv preprint arXiv:1605.08361, 2016.<br />
<br />
Daniel Soudry and Elad Hoffer. Exponentially vanishing sub-optimal local minima in multilayer neural networks. arXiv preprint arXiv:1702.05777, 2017.<br />
<br />
Daniel Soudry, Elad Hoffer, and Nathan Srebro. The implicit bias of gradient descent on separable data. 2018.<br />
<br />
Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.<br />
<br />
Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. arXiv preprint arXiv:1707.02968, 2017.<br />
<br />
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1–9, 2015.<br />
<br />
Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2818–2826, 2016.<br />
<br />
Cheng Tai, Tong Xiao, Yi Zhang, Xiaogang Wang, et al. Convolutional neural networks with lowrank regularization. arXiv preprint arXiv:1511.06067, 2015.<br />
<br />
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2017.<br />
Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
Bo Xie, Yingyu Liang, and Le Song. Diversity leads to generalization in neural networks. arXiv preprint arXiv:1611.03131, 2016.<br />
<br />
Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European conference on computer vision, pp. 818–833. Springer, 2014. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017a. URL https://arxiv.org/abs/1611.03530.<br />
<br />
Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. arXiv preprint arXiv:1707.01083, 2017b.<br />
<br />
Shuchang Zhou, Zekun Ni, Xinyu Zhou, He Wen, Yuxin Wu, and Yuheng Zou. Dorefa-net: Training low bitwidth convolutional neural networks with low bitwidth gradients. arXiv preprint arXiv:1606.06160, 2016.<br />
<br />
A. Rosenfeld and J. K. Tsotsos, “Intriguing properties of randomly weighted networks: Generalizing while learning next to nothing,” arXiv preprint arXiv:1802.00844, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fix_your_classifier:_the_marginal_value_of_training_the_last_weight_layer&diff=42211Fix your classifier: the marginal value of training the last weight layer2018-12-02T23:11:54Z<p>A22ravi: /* Introduction */</p>
<hr />
<div><br />
The code for the proposed model is available at https://github.com/eladhoffer/fix_your_classifier.<br />
<br />
=Introduction=<br />
<br />
Deep neural networks have become widely used for machine learning, achieving state-of-the-art results on many tasks. One of the most common tasks they are used for is classification. For example, convolutional neural networks (CNNs) are used to classify images to a semantic category. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more computational resources. Thus, extensive amount of research has been done lately to reduce the size of networks. Han et al. (2015) used weight sharing and specification, Micikevicius et al. (2017) used mixed precision to reduce the size of the neural networks by half. Tai et al. (2015) and Jaderberg et al. (2014) used low rank approximations to speed up NNs. Hubara et al. (2016b), Li et al. (2016) and Zhou et al. (2016), used a more aggressive approach, in which weights, activations and gradients were quantized to further reduce computation during training. Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
Past work noted the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on several tasks. This study suggests the reverse proposal - that common NN models used can learn useful representation even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Brief Overview=<br />
<br />
In order to alleviate the aforementioned problem, the authors propose that the final layer of the classifier be fixed (up to a global scale constant). They argue that with little or no loss of accuracy for most classification tasks, the method provides significant memory and computational benefits. In addition, they show that by initializing the classifier with a Hadamard matrix the inference could be made faster as well.<br />
<br />
=Previous Work=<br />
<br />
Training NN models and using them for inference requires large amounts of memory and computational resources; thus, extensive amount of research has been done lately to reduce the size of networks which are as follows:<br />
<br />
* Weight sharing and specification (Han et al., 2015)<br />
<br />
* Mixed precision to reduce the size of the neural networks by half (Micikevicius et al., 2017)<br />
<br />
* Low-rank approximations to speed up CNN (Tai et al., 2015)<br />
<br />
* Quantization of weights, activations, and gradients to further reduce computation during training (Hubara et al., 2016b; Li et al., 2016 and Zhou et al., 2016)<br />
<br />
Some of the past works have also put forward the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on many of the classification tasks. However, the authors' proposal in the current paper is quite reversed.<br />
<br />
=Background=<br />
<br />
A Convolutional Neural Network (CNN) is comprised of one or more convolutional layers (often with a subsampling step) and then followed by one or more fully connected layers as in a standard multilayer neural network. The architecture of a CNN is designed to take advantage of the 2D structure of an input image (or other 2D input such as a speech signal). This is achieved with local connections and tied weights followed by some form of pooling which results in translation invariant features. Another benefit of CNNs is that they are easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. <br />
<br />
A CNN consists of a number of convolutional and subsampling layers optionally followed by fully connected layers. The input to a convolutional layer is a <math>m \times m \times r</math> image where m is the height and width of the image and <math>r</math> is the number of channels, e.g. an RGB image has <math>r=3</math>. The convolutional layer will have <math>k</math> filters (or kernels) of size <math>n \times n \times q</math> where <math>n</math> is smaller than the dimension of the image and <math>q</math> can either be the same as the number of channels <math>r</math> or smaller and may vary for each kernel. The size of the filters gives rise to the locally connected structure which are each convolved with the image to produce <math>k</math> feature maps of size <math>m−n+1</math>. Each map is then subsampled typically with mean or max pooling over <math>p \times p</math> contiguous regions where <math>p</math> ranges between 2 for small images (e.g. MNIST) and is usually not more than 5 for larger inputs. Either before or after the subsampling layer an additive bias and sigmoidal nonlinearity is applied to each feature map. <br />
<br />
CNNs are commonly used to solve a variety of spatial and temporal tasks. Earlier architectures of CNNs (LeCun et al., 1998; Krizhevsky et al., 2012) used a set of fully-connected layers at later stages of the network, presumably to allow classification based on global features of an image.<br />
<br />
<br />
<br />
== Shortcomings of the Final Classification Layer and its Solution ==<br />
<br />
Zeiler & Fergus, 2014 showed that despite the enormous number of trainable parameters these layers add to the model, they are known to have a rather marginal impact on the final performance of the network.<br />
<br />
It has been shown previously that these layers could be easily compressed and reduced after a model was trained by simple means such as matrix decomposition and sparsification (Han et al., 2015). Modern architecture choices are characterized with the removal of most of the fully connected layers (Lin et al., 2013; Szegedy et al., 2015; He et al., 2016), that lead to better generalization and overall accuracy, together with a huge decrease in the number of trainable parameters. Additionally, numerous works showed that CNNs can be trained in a metric learning regime (Bromley et al., 1994; Schroff et al., 2015; Hoffer & Ailon, 2015), where no explicit classification layer was introduced and the objective regarded only distance measures between intermediate representations. Hardt & Ma (2017) suggested an all-convolutional network variant, where they kept the original initialization of the classification layer fixed with no negative impact on performance on the CIFAR-10 dataset.<br />
<br />
=Proposed Method=<br />
<br />
The aforementioned works provide evidence that fully-connected layers are in fact redundant and play a small role in learning and generalization. In this work, the authors have suggested that the parameters used for the final classification transform are completely redundant, and can be replaced with a predetermined linear transform. This holds for even in large-scale models and classification tasks, such as recent architectures trained on the ImageNet benchmark (Deng et al., 2009).<br />
<br />
==Using a Fixed Classifier==<br />
<br />
Suppose the final representation obtained by the network (the last hidden layer) is represented as <math>x = F(z;\theta)</math> where <math>F</math> is assumed to be a deep neural network with input z and parameters θ, e.g., a convolutional network, trained by backpropagation.<br />
<br />
In common NN models, this representation is followed by an additional affine transformation, <math>y = W^T x + b</math> ,where <math>W</math> and <math>b</math> are also trained by back-propagation.<br />
<br />
For input <math>x</math> of <math>N</math> length, and <math>C</math> different possible outputs, <math>W</math> is required to be a matrix of <math>N ×<br />
C</math>. Training is done using cross-entropy loss, by feeding the network outputs through a softmax activation<br />
<br />
<math><br />
v_i = \frac{e^{y_i}}{\sum_{j}^{C}{e^{y_j}}}, i &isin; </math> { <math> {1, . . . , C} </math> }<br />
<br />
and reducing the expected negative log likelihood with respect to ground-truth target <math> t &isin; </math> { <math> {1, . . . , C} </math> },<br />
by minimizing the loss function:<br />
<br />
<math><br />
L(x, t) = −\text{log}\ {v_t} = −{w_t}·{x} − b_t + \text{log} ({\sum_{j}^{C}e^{w_j . x + b_j}})<br />
</math><br />
<br />
where <math>w_i</math> is the <math>i</math>-th column of <math>W</math>.<br />
<br />
==Choosing the Projection Matrix==<br />
<br />
To evaluate the conjecture regarding the importance of the final classification transformation, the trainable parameter matrix <math>W</math> is replaced with a fixed orthonormal projection <math> Q &isin; R^{N×C} </math>, such that <math> &forall; i &ne; j : q_i · q_j = 0 </math> and <math> || q_i ||_{2} = 1 </math>, where <math>q_i</math> is the <math>i</math>th column of <math>Q</math>. This is ensured by a simple random sampling and singular-value decomposition<br />
<br />
As the rows of classifier weight matrix are fixed with an equally valued <math>L_{2}</math> norm, we find it beneficial<br />
to also restrict the representation of <math>x</math> by normalizing it to reside on the <math>n</math>-dimensional sphere:<br />
<br />
<center><math><br />
\hat{x} = \frac{x}{||x||_{2}}<br />
</math></center><br />
<br />
This allows faster training and convergence, as the network does not need to account for changes in the scale of its weights. However, it has now an issue that <math>q_i · \hat{x} </math> is bounded between −1 and 1. This causes convergence issues, as the softmax function is scale sensitive, and the network is affected by the inability to re-scale its input. This issue is amended with a fixed scale <math>T</math> applied to softmax inputs <math>f(y) = softmax(\frac{1}{T}y)</math>, also known as the ''softmax temperature''. However, this introduces an additional hyper-parameter which may differ between networks and datasets. So, the authors propose to introduce a single scalar parameter <math>\alpha</math> to learn the softmax scale, effectively functioning as an inverse of the softmax temperature <math>\frac{1}{T}</math>. The normalized weights and an additional scale coefficient are also used, specially using a single scale for all entries in the weight matrix. The additional vector of bias parameters <math>b &isin; \mathbb{R}^{C}</math> is kept the same and the model is trained using the traditional negative-log-likelihood criterion. Explicitly, the classifier output is now:<br />
<br />
<center><br />
<math><br />
v_i=\frac{e^{\alpha q_i &middot; \hat{x} + b_i}}{\sum_{j}^{C} e^{\alpha q_j &middot; \hat{x} + b_j}}, i &isin; </math> { <math> {1,...,C} </math>}<br />
</center><br />
<br />
and the loss to be minimized is:<br />
<br />
<center><math><br />
L(x, t) = -\alpha q_t &middot; \frac{x}{||x||_{2}} + b_t + \text{log} (\sum_{i=1}^{C} \text{exp}((\alpha q_i &middot; \frac{x}{||x||_{2}} + b_i)))<br />
</math></center><br />
<br />
where <math>x</math> is the final representation obtained by the network for a specific sample, and <math> t &isin; </math> { <math> {1, . . . , C} </math> } is the ground-truth label for that sample. The behaviour of the parameter <math> \alpha </math> over time, which is logarithmic in nature and has the same behavior exhibited by the norm of a learned classifier, is shown in<br />
[[Media: figure1_log_behave.png| Figure 1]].<br />
<br />
<center>[[File:figure1_log_behave.png]]</center><br />
<br />
When <math> -1 \le q_i · \hat{x} \le 1 </math>, a possible cosine angle loss is <br />
<br />
<center>[[File:caloss.png]]</center><br />
<br />
But its final validation accuracy has a slight decrease, compared to original models.<br />
<br />
==Using a Hadmard Matrix==<br />
<br />
To recall, Hadmard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are either +1 or −1.<br />
Furthermore, <math> H </math> is orthogonal, such that <math> HH^{T} = nI_n </math> where <math>I_n</math> is the identity matrix. Instead of using the entire Hadmard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all <math>C</math> rows are orthogonal as the final classification layer is such that:<br />
<br />
<center><math><br />
y = \hat{H} \hat{x} + b<br />
</math></center><br />
<br />
This usage allows two main benefits:<br />
* A deterministic, low-memory and easily generated matrix that can be used for classification.<br />
* Removal of the need to perform a full matrix-matrix multiplication - as multiplying by a Hadamard matrix can be done by simple sign manipulation and addition.<br />
<br />
Here, <math>n</math> must be a multiple of 4, but it can be easily truncated to fit normally defined networks. Also, as the classifier weights are fixed to need only 1-bit precision, it is now possible to focus our attention on the features preceding it.<br />
<br />
=Experimental Results=<br />
<br />
The authors have evaluated their proposed model on the following datasets:<br />
<br />
==CIFAR-10/100==<br />
<br />
===About the Dataset===<br />
<br />
CIFAR-10 is an image classification benchmark dataset containing 50,000 training images and 10,000 test images. The images are in color and contain 32×32 pixels. There are 10 possible classes of various animals and vehicles. CIFAR-100 holds the same number of images of the same size, but contains 100 different classes.<br />
<br />
===Training Details===<br />
<br />
The authors trained a residual network ( He et al., 2016) on the CIFAR-10 dataset. The network depth was 56 and the same hyper-parameters as in the original work were used. A comparison of the two variants, i.e., the learned classifier and the proposed classifier with a fixed transformation is shown in [[Media: figure1_resnet_cifar10.png | Figure 2]].<br />
<br />
<center>[[File: figure1_resnet_cifar10.png]]</center><br />
<br />
These results demonstrate that although the training error is considerably lower for the network with learned classifier, both models achieve the same classification accuracy on the validation set. The authors' conjecture is that with the new fixed parameterization, the network can no longer increase the norm of a given sample’s representation - thus learning its label requires more effort. As this may happen for specific seen samples - it affects only training error.<br />
<br />
The authors also compared using a fixed scale variable <math>\alpha </math> at different values vs. the learned parameter. Results for <math> \alpha = </math> {0.1, 1, 10} are depicted in [[Media: figure3_alpha_resnet_cifar.png| Figure 3]] for both training and validation error and as can be seen, similar validation accuracy can be obtained using a fixed scale value (in this case <math>\alpha </math>= 1 or 10 will suffice) at the expense of another hyper-parameter to seek. In all the further experiments the scaling parameter <math> \alpha </math> was regularized with the same weight decay coefficient used on original classifier. Although learning the scale is not necessary, but it will help convergence during training.<br />
<br />
<center>[[File: figure3_alpha_resnet_cifar.png]]</center><br />
<br />
The authors then train the model on CIFAR-100 dataset. They used the DenseNet-BC model from Huang et al. (2017) with a depth of 100 layers and k = 12. The higher number of classes caused the number of parameters to grow and encompassed about 4% of the whole model. However, validation accuracy for the fixed-classifier model remained equally good as the original model, and the same training curve was observed as earlier.<br />
<br />
==IMAGENET==<br />
<br />
===About the Dataset===<br />
<br />
The Imagenet dataset introduced by Deng et al. (2009) spans over 1000 visual classes, and over 1.2 million samples. This is supposedly a more challenging dataset to work on as compared to CIFAR-10/100.<br />
<br />
===Experiment Details===<br />
<br />
The authors evaluated their fixed classifier method on Imagenet using Resnet50 by He et al. (2016) and Densenet169 model (Huang et al., 2017) as described in the original work. Using a fixed classifier removed approximately 2-million parameters were from the model, accounting for about 8% and 12 % of the model parameters respectively. The experiments revealed similar trends as observed on CIFAR-10.<br />
<br />
For a more stricter evaluation, the authors also trained a Shufflenet architecture (Zhang et al., 2017b), which was designed to be used in low memory and limited computing platforms and has parameters making up the majority of the model. They were able to reduce the parameters to 0.86 million as compared to 0.96 million parameters in the final layer of the original model. Again, the proposed modification in the original model gave similar convergence results on validation accuracy. Interestingly, this method allowed Imagenet training in an under-specified regime, where there are<br />
more training samples than the number of parameters. This is an unconventional regime for modern deep networks, which are usually over-specified to have many more parameters than training samples (Zhang et al., 2017a).<br />
<br />
The overall results of the fixed-classifier are summarized in [[Media: table1_fixed_results.png | Table 1]].<br />
<br />
<center>[[File: table1_fixed_results.png]]</center><br />
<br />
==Language Modelling==<br />
<br />
Recent works have empirically found that using the same weights for both word embedding and classifier can yield equal or better results than using a separate pair of weights. So the authors experimented with fix-classifiers on language modeling as it also requires classification of all possible tokens available in the task vocabulary. They trained a recurrent model with 2-layers of LSTM (Hochreiter & Schmidhuber, 1997) and embedding + hidden size of 512 on the WikiText2 dataset (Merity et al., 2016), using same settings as in Merity et al. (2017). WikiText2 dataset contains about 33K different words, so the number of parameters expected in the embedding and classifier layer was about 34-million. This number is about 89% of the total number of parameters used for the whole model which is 38-million. However, using a random orthogonal transform yielded poor results compared to learned embedding. This was suspected to be due to semantic relationships captured in the embedding layer of language models, which is not the case in image classification task. The intuition was further confirmed by the much better results when pre-trained embeddings using word2vec algorithm by Mikolov et al. (2013) or PMI factorization as suggested by Levy & Goldberg (2014), were used. The final result used 89% fewer parameters than a fully learned model, with only marginally worse perplexity. The authors posit that this implies a required structure in word embedding that originates from the semantic relatedness between words, and unbalanced classes. They further suggest that with more efficient ways to train word embeddings, it may be possible to mitigate the issues arising from this structure and class imbalance. <br />
<br />
<center>[[File: language.png]]</center><br />
<br />
=Discussion=<br />
<br />
==Implications and Use Cases==<br />
<br />
With the increasing number of classes in the benchmark datasets, computational demands for the final classifier will increase as well. In order to understand the problem better, the authors observe the work by Sun et al. (2017), which introduced JFT-300M - an internal Google dataset with over 18K different classes. Using a Resnet50 (He et al., 2016), with a 2048 sized representation led to a model with over 36M parameters meaning that over 60% of the model parameters resided in the final classification layer. Sun et al. (2017) also describe the difficulty in distributing so many parameters over the training servers involving a non-trivial overhead during synchronization of the model for update. The authors claim that the fixed-classifier would help considerably in this kind of scenario - where using a fixed classifier removes the need to do any gradient synchronization for the final layer. Furthermore, introduction of Hadamard matrix removes the need to save the transformation altogether, thereby, making it more efficient and allowing considerable memory and computational savings.<br />
<br />
==Possible Caveats==<br />
<br />
The good performance of fixed-classifiers relies on the ability of the preceding layers to learn separable representations. This could be affected when the ratio between learned features and number of classes is small – that is, when <math> C > N</math>. However, they tested their method in such cases and their model performed well and provided good results.<br />
Another factor that can affect the performance of their model using a fixed classifier is when the classes are highly correlated. In that case, the fixed classifier actually cannot support correlated classes and thus, the network could have some difficulty to learn. For a language model, word classes tend to have highly correlated instances, which also lead to difficult learning process.<br />
<br />
Also, this proposed approach will only eliminate the computation of the classifier weights, so when the classes are fewer, the computation saving effect will not be readily apparent.<br />
<br />
==Future Work==<br />
<br />
<br />
The use of fixed classifiers might be further simplified in Binarized Neural Networks (Hubara et al., 2016a), where the activations and weights are restricted to ±1 during propagations. In that case, the norm of the last hidden layer would be constant for all samples (equal to the square root of the hidden layer width). The constant could then be absorbed into the scale constant <math>\alpha</math>, and there is no need in a per-sample normalization.<br />
<br />
Additionally, more efficient ways to learn a word embedding should also be explored where similar redundancy in classifier weights may suggest simpler forms of token representations - such as low-rank or sparse versions.<br />
<br />
A related paper was published that claims that fixing most of the parameters of the neural network achieves comparable results with learning all of them [A. Rosenfeld and J. K. Tsotsos]<br />
<br />
=Conclusion=<br />
<br />
In this work, the authors argue that the final classification layer in deep neural networks is redundant and suggest removing the parameters from the classification layer. The empirical results from experiments on the CIFAR and IMAGENET datasets suggest that such a change lead to little or almost no decline in the performance of the architecture. Furthermore, using a Hadmard matrix as classifier might lead to some computational benefits when properly implemented, and save memory otherwise spent on large amount of transformation coefficients.<br />
<br />
Another possible scope of research that could be pointed out for future could be to find new efficient methods to create pre-defined word embeddings, which require huge amount of parameters that can possibly be avoided when learning a new task. Therefore, more emphasis should be given to the representations learned by the non-linear parts of the neural networks - up to the final classifier, as it seems highly redundant.<br />
<br />
=Critique=<br />
<br />
The paper proposes an interesting idea that has a potential use case when designing memory-efficient neural networks. The experiments shown in the paper are quite rigorous and provide support to the authors' claim. However, it would have been more helpful if the authors had described a bit more about efficient implementation of the Hadamard matrix and how to scale this method for larger datasets (cases with <math> C >N</math>).<br />
<br />
Moreover, one of the main intuitions of the paper has introduced to be computational cost but it has left out to compare a fixed and learned classifier based on the computational cost and then investigate whether it worth the drop in performance or not considering the fact that not always the output can be degraded because of need for speed! At least a discussion on this issue is expected.<br />
<br />
On the other hand, the computational cost and performance change after fixation of classifier could be related to dataset and the nature and complexity of it. Mostly, having 1000 classes makes the classification more crucial than 2 classes. An evaluation of this topic is also needed.<br />
<br />
Another interesting experiment to do would be to look this technique interacts with distillation when used in the teacher or student network or both. For instance, Does fixing the features make it more difficult to place dog than on boat when classifying a cat? Do networks with fixed classifier weights make worse teachers for distillation?<br />
<br />
=References=<br />
<br />
Madhu S Advani and Andrew M Saxe. High-dimensional dynamics of generalization error in neural networks. arXiv preprint arXiv:1710.03667, 2017.<br />
<br />
Peter Bartlett, Dylan J Foster, and Matus Telgarsky. Spectrally-normalized margin bounds for neural networks. arXiv preprint arXiv:1706.08498, 2017.<br />
<br />
Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Sackinger, and Roopak Shah. Signature verification using a” siamese” time delay neural network. In Advances in Neural Information Processing Systems, pp. 737–744, 1994.<br />
<br />
Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Binaryconnect: Training deep neural networks with binary weights during propagations. In Advances in Neural Information Processing Systems, pp. 3123–3131, 2015.<br />
<br />
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 248–255. IEEE, 2009.<br />
<br />
Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro. Implicit regularization in matrix factorization. arXiv preprint arXiv:1705.09280, 2017.<br />
<br />
Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.<br />
<br />
Moritz Hardt and Tengyu Ma. Identity matters in deep learning. 2017.<br />
<br />
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.<br />
<br />
A Hedayat, WD Wallis, et al. Hadamard matrices and their applications. The Annals of Statistics, 6<br />
(6):1184–1238, 1978.<br />
<br />
Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.<br />
<br />
Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International Workshop on Similarity-Based Pattern Recognition, pp. 84–92. Springer, 2015.<br />
<br />
Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. 2017.<br />
<br />
Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017.<br />
<br />
Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017.<br />
<br />
Guang-Bin Huang, Qin-Yu Zhu, and Chee-Kheong Siew. Extreme learning machine: theory and applications. Neurocomputing, 70(1):489–501, 2006.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. In Advances in Neural Information Processing Systems 29 (NIPS’16), 2016a.<br />
<br />
Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Quantized neural networks: Training neural networks with low precision weights and activations. arXiv preprint arXiv:1609.07061, 2016b.<br />
<br />
Hakan Inan, Khashayar Khosravi, and Richard Socher. Tying word vectors and word classifiers: A loss framework for language modeling. arXiv preprint arXiv:1611.01462, 2016.<br />
<br />
Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. arXiv preprint arXiv:1405.3866, 2014.<br />
<br />
Alex Krizhevsky. Learning multiple layers of features from tiny images. 2009.<br />
<br />
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012.<br />
<br />
Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278 2324, 1998.<br />
<br />
Omer Levy and Yoav Goldberg. Neural word embedding as implicit matrix factorization. In Advances in neural information processing systems, pp. 2177–2185, 2014.<br />
<br />
Fengfu Li, Bo Zhang, and Bin Liu. Ternary weight networks. arXiv preprint arXiv:1605.04711, 2016.<br />
<br />
Min Lin, Qiang Chen, and Shuicheng Yan. Network in network. arXiv preprint arXiv:1312.4400, 2013.<br />
<br />
Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. arXiv preprint arXiv:1609.07843, 2016.<br />
<br />
Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017.<br />
<br />
Paulius Micikevicius, Sharan Narang, Jonah Alben, Gregory Diamos, Erich Elsen, David Garcia, Boris Ginsburg, Michael Houston, Oleksii Kuchaev, Ganesh Venkatesh, et al. Mixed precision training. arXiv preprint arXiv:1710.03740, 2017.<br />
<br />
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed tations of words and phrases and their compositionality. In Advances in neural information processing systems, pp. 3111–3119, 2013.<br />
<br />
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring generalization in deep learning. arXiv preprint arXiv:1706.08947, 2017.<br />
Jooyoung Park and Irwin W Sandberg. Universal approximation using radial-basis-function networks. Neural computation, 3(2):246–257, 1991.<br />
<br />
Ofir Press and Lior Wolf. Using the output embedding to improve language models. EACL 2017,<br />
pp. 157, 2017.<br />
<br />
Itay Safran and Ohad Shamir. On the quality of the initial basin in overspecified neural networks. In International Conference on Machine Learning, pp. 774–782, 2016.<br />
<br />
Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016.<br />
<br />
Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 815–823, 2015.<br />
<br />
Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. arXiv preprint arXiv:1707.04926, 2017.<br />
<br />
Daniel Soudry and Yair Carmon. No bad local minima: Data independent training error guarantees for multilayer neural networks. arXiv preprint arXiv:1605.08361, 2016.<br />
<br />
Daniel Soudry and Elad Hoffer. Exponentially vanishing sub-optimal local minima in multilayer neural networks. arXiv preprint arXiv:1702.05777, 2017.<br />
<br />
Daniel Soudry, Elad Hoffer, and Nathan Srebro. The implicit bias of gradient descent on separable data. 2018.<br />
<br />
Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.<br />
<br />
Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. arXiv preprint arXiv:1707.02968, 2017.<br />
<br />
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1–9, 2015.<br />
<br />
Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2818–2826, 2016.<br />
<br />
Cheng Tai, Tong Xiao, Yi Zhang, Xiaogang Wang, et al. Convolutional neural networks with lowrank regularization. arXiv preprint arXiv:1511.06067, 2015.<br />
<br />
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2017.<br />
Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
Bo Xie, Yingyu Liang, and Le Song. Diversity leads to generalization in neural networks. arXiv preprint arXiv:1611.03131, 2016.<br />
<br />
Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European conference on computer vision, pp. 818–833. Springer, 2014. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017a. URL https://arxiv.org/abs/1611.03530.<br />
<br />
Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. arXiv preprint arXiv:1707.01083, 2017b.<br />
<br />
Shuchang Zhou, Zekun Ni, Xinyu Zhou, He Wen, Yuxin Wu, and Yuheng Zou. Dorefa-net: Training low bitwidth convolutional neural networks with low bitwidth gradients. arXiv preprint arXiv:1606.06160, 2016.<br />
<br />
A. Rosenfeld and J. K. Tsotsos, “Intriguing properties of randomly weighted networks: Generalizing while learning next to nothing,” arXiv preprint arXiv:1802.00844, 2018.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DON%27T_DECAY_THE_LEARNING_RATE_,_INCREASE_THE_BATCH_SIZE&diff=42032DON'T DECAY THE LEARNING RATE , INCREASE THE BATCH SIZE2018-11-30T11:03:45Z<p>A22ravi: /* CONCLUSIONS */</p>
<hr />
<div>Summary of the ICLR 2018 paper: '''Don't Decay the learning Rate, Increase the Batch Size ''' <br />
<br />
Link: [https://arxiv.org/pdf/1711.00489.pdf]<br />
<br />
Summarized by: Afify, Ahmed [ID: 20700841]<br />
<br />
==INTUITION==<br />
Nowadays, it is a common practice not to have a singular steady learning rate for the learning phase of neural network models. Instead, we use adaptive learning rates with the standard gradient descent method. The intuition behind this is that when we are far away from the minima, it is beneficial for us to take large steps towards the minima, as it would require a lesser number of steps to converge, but as we approach the minima, our step size should decrease, otherwise we may just keep oscillating around the minima. In practice, this is generally achieved by methods like SGD with momentum, Nesterov momentum, and Adam. However, the core claim of this paper is that the same effect can be achieved by increasing the batch size during the gradient descent process while keeping the learning rate constant throughout. In addition, the paper argues that such an approach also reduces the parameter updates required to reach the minima, thus leading to greater parallelism and shorter training times.<br />
<br />
== INTRODUCTION ==<br />
Stochastic gradient descent (SGD) is the most widely used optimization technique for training deep learning models. The reason for this is that the minima found using this process generalizes well (Zhang et al., 2016; Wilson et al., 2017), but the optimization process is slow and time consuming. According to (Goyal et al., 2017; Hoffer et al., 2017; You et al., 2017a), this has motivated researchers to try to speed up this optimization process by taking bigger steps, and hence reduce the number of parameter updates in training a model. This can be achieved by using large batch training, which can be divided across many machines. <br />
<br />
However, increasing the batch size leads to decreasing the test set accuracy (Keskar et al., 2016; Goyal et al., 2017). Smith and Le (2017) believed that SGD has a scale of random fluctuations <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N number of training samples, and B batch size. They concluded that there is an optimal batch size proportional to the learning rate when <math> B \ll N </math>, and optimum fluctuation scale <math>g</math> for a maximum test set accuracy.<br />
<br />
In this paper, the authors' main goal is to provide evidence that increasing the batch size is quantitatively equivalent to decreasing the learning rate with the same number of training epochs in decreasing the scale of random fluctuations, but with remarkably less number of parameter updates. Moreover, an additional reduction in the number of parameter updates can be attained by increasing the learning rate and scaling <math> B \propto \epsilon </math> or even more reduction by increasing the momentum coefficient and scaling <math> B \propto \frac{1}{1-m} </math> although the latter decreases the test accuracy. This has been demonstrated by several experiments on the ImageNet and CIFAR-10 datasets using ResNet-50 and Inception-ResNet-V2 architectures respectively.<br />
<br />
== STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION ==<br />
As mentioned in the previous section, the drawback of SGD when compared to full-batch training is the noise that it introduces that hinders optimization. According to (Robbins & Monro, 1951), there are two equations that govern how to reach the minimum of a convex function: (<math> \epsilon_i </math> denotes the learning rate at the <math> i^{th} </math> gradient update)<br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon_i = \infty </math>. This equation guarantees that we will reach the minimum. <br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon^2_i < \infty </math>. This equation, which is valid only for a fixed batch size, guarantees that learning rate decays fast enough allowing us to reach the minimum rather than bouncing due to noise.<br />
<br />
These equations indicate that the learning rate must decay during training, and second equation is only available when the batch size is constant. To change the batch size, Smith and Le (2017) proposed to interpret SGD as integrating this stochastic differential equation <math> \frac{dw}{dt} = -\frac{dC}{dw} + \eta(t) </math>, where <math>C</math> represents cost function, <math>w</math> represents the parameters, and <math>\eta</math> represents the Gaussian random noise. Furthermore, they proved that noise scale <math>g</math> controls the magnitude of random fluctuations in the training dynamics by this formula: <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N is the training set size and <math>B</math> is the batch size. As we usually have <math> B \ll N </math>, we can define <math> g \approx \epsilon \frac{N}{B} </math>. This explains why when the learning rate decreases, noise <math>g</math> decreases, enabling us to converge to the minimum of the cost function. However, increasing the batch size has the same effect and makes <math>g</math> decays with constant learning rate. In this work, the batch size is increased until <math> B \approx \frac{N}{10} </math>, then the conventional way of decaying the learning rate is followed.<br />
<br />
== SIMULATED ANNEALING AND THE GENERALIZATION GAP ==<br />
'''Simulated Annealing:''' decaying learning rates are empirically successful. To understand this, they note that introducing random fluctuations<br />
whose scale falls during training is also a well established technique in non-convex optimization; simulated annealing. The initial noisy optimization phase allows to explore a larger fraction of the parameter space without becoming trapped in local minima. Once a promising region of parameter space is located, the noise is reduced to fine-tune the parameters.<br />
<br />
For more info: Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as gradient descent. [https://en.wikipedia.org/wiki/Simulated_annealing [Reference]]<br />
<br />
'''Generalization Gap:''' Small batch data generalizes better to the test set than large batch data.<br />
<br />
Smith and Le (2017) found that there is an optimal batch size which corresponds to optimal noise scale g <math> (g \approx \epsilon \frac{N}{B}) </math> and concluded that <math> B_{opt} \propto \epsilon N </math> that corresponds to maximum test set accuracy. This means that gradient noise is helpful as it makes SGD escape sharp minima, which does not generalize well. <br />
<br />
Simulated Annealing is a famous technique in non-convex optimization. Starting with noise in the training process helps us to discover a wide range of parameters then once we are near the optimum value, noise is reduced to fine tune our final parameters. However, more and more researches like to use the sharper decay schedules like cosine decay or step-function drops. In physical sciences, slowly annealing (or decaying) the temperature (which is the noise scale in this situation) helps to converge to the global minimum, which is sharp. But decaying the temperature in discrete steps can make the system stuck in a local minimum, which lead to higher cost and lower curvature. The authors think that deep learning has the same intuition.<br />
.<br />
<br />
== THE EFFECTIVE LEARNING RATE AND THE ACCUMULATION VARIABLE ==<br />
'''The Effective Learning Rate''' : <math> \epsilon_{eff} = \frac{\epsilon}{1-m} </math><br />
<br />
Smith and Le (2017) included momentum to the equation of the vanilla SGD noise scale that was defined above to be: <math> g = \frac{\epsilon}{1-m}(\frac{N}{B}-1)\approx \frac{\epsilon N}{B(1-m)} </math>, which is the same as the previous equation when m goes to 0. They found that increasing the learning rate and momentum coefficient and scaling <math> B \propto \frac{\epsilon }{1-m} </math> reduces the number of parameter updates, but the test accuracy decreases when the momentum coefficient is increased. <br />
<br />
To understand the reasons behind this, we need to analyze momentum update equations below:<br />
<br />
<center><math><br />
\Delta A = -(1-m)A + \frac{d\widehat{C}}{dw} <br />
</math><br />
<br />
<math><br />
\Delta w = -A\epsilon<br />
</math><br />
</center><br />
<br />
We can see that the Accumulation variable A, which is initially set to 0, then increases exponentially to reach its steady state value during <math> \frac{B}{N(1-m)} </math> training epochs while <math> \Delta w </math> is suppressed that can reduce the rate of convergence. Moreover, at high momentum, we have three challenges:<br />
<br />
1- Additional epochs are needed to catch up with the accumulation.<br />
<br />
2- Accumulation needs more time <math> \frac{B}{N(1-m)} </math> to forget old gradients. <br />
<br />
3- After this time, however, the accumulation cannot adapt to changes in the loss landscape.<br />
<br />
4- In the early stage, large batch size will lead to the instabilities.<br />
<br />
== EXPERIMENTS ==<br />
=== SIMULATED ANNEALING IN A WIDE RESNET ===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Schedules used as in the below figure:''' <br />
<br />
- Decaying learning rate: learning rate decays by a factor of 5 at a sequence of “steps”, and the batch size is constant<br />
<br />
- Increasing batch size: learning rate is constant, and the batch size is increased by a factor of 5 at every step.<br />
<br />
- Hybrid: At the beginning, the learning rate is constant and batch size is increased by a factor of 5. Then, the learning rate decays by a factor of 5 at each subsequent step, and the batch size is constant. This is the schedule that will be used if there is a hardware limit affecting a maximum batch size limit.<br />
<br />
[[File:Paper_40_Fig_1.png | 800px|center]]<br />
<br />
As shown in the below figure: in the left figure (2a), we can observe that for the training set, the three learning curves are exactly the same while in figure 2b, increasing the batch size has a huge advantage of reducing the number of parameter updates.<br />
This concludes that noise scale is the one that needs to be decayed and not the learning rate itself<br />
[[File:Paper_40_Fig_2.png | 800px|center]] <br />
<br />
To make sure that these results are the same for the test set as well, in figure 3, we can see that the three learning curves are exactly the same for SGD with momentum, and Nesterov momentum<br />
[[File:Paper_40_Fig_3.png | 800px|center]]<br />
<br />
To check for other optimizers as well. the below figure shows the same experiment as in figure 3, which is the three learning curves for test set, but for vanilla SGD and Adam, and showing <br />
[[File:Paper_40_Fig_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Decreasing the learning rate and increasing the batch size during training are equivalent<br />
<br />
=== INCREASING THE EFFECTIVE LEARNING RATE===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Parameters:''' Optimization Algorithm: SGD with momentum / Maximum batch size = 5120<br />
<br />
'''Training Schedules:''' <br />
<br />
The authors consider four training schedules, all of which decay the noise scale by a factor of five in a series of three steps with the same number of epochs.<br />
<br />
Original training schedule: initial learning rate of 0.1 which decays by a factor of 5 at each step, a momentum coefficient of 0.9, and a batch size of 128. <br />
<br />
Increasing batch size: learning rate of 0.1, momentum coefficient of 0.9, initial batch size of 128 that increases by a factor of 5 at each step. <br />
<br />
Increased initial learning rate: initial learning rate of 0.5, initial batch size of 640 that increase during training.<br />
<br />
Increased momentum coefficient: increased initial learning rate of 0.5, initial batch size of 3200 that increase during training, and an increased momentum coefficient of 0.98.<br />
<br />
The results of all training schedules, which are presented in the below figure, are documented in the following table:<br />
<br />
[[File:Paper_40_Table_1.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_5.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the effective learning rate and scaling the batch size results in further reduction in the number of parameter updates<br />
<br />
=== TRAINING IMAGENET IN 2500 PARAMETER UPDATES===<br />
<br />
'''A) Experiment Goal:''' Control Batch Size<br />
<br />
'''Dataset:''' ImageNet (1.28 million training images)<br />
<br />
The paper modified the setup of Goyal et al. (2017), and used the following configuration:<br />
<br />
'''Network Architecture:''' Inception-ResNet-V2 <br />
<br />
'''Training Parameters:''' <br />
<br />
90 epochs / noise decayed at epoch 30, 60, and 80 by a factor of 10 / Initial ghost batch size = 32 / Learning rate = 3 / momentum coefficient = 0.9 / Initial batch size = 8192<br />
<br />
Two training schedules were used:<br />
<br />
“Decaying learning rate”, where batch size is fixed and the learning rate is decayed<br />
<br />
“Increasing batch size”, where batch size is increased to 81920 then the learning rate is decayed at two steps.<br />
<br />
[[File:Paper_40_Table_2.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_6.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the batch size resulted in reducing the number of parameter updates from 14,000 to 6,000.<br />
<br />
'''B) Experiment Goal:''' Control Batch Size and Momentum Coefficient<br />
<br />
'''Training Parameters:''' Ghost batch size = 64 / noise decayed at epoch 30, 60, and 80 by a factor of 10. <br />
<br />
The below table shows the number of parameter updates and accuracy for different set of training parameters:<br />
<br />
[[File:Paper_40_Table_3.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_7.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the momentum reduces the number of parameter updates, but leads to a drop in the test accuracy.<br />
<br />
=== TRAINING IMAGENET IN 30 MINUTES===<br />
<br />
'''Dataset:''' ImageNet (Already introduced in the previous section)<br />
<br />
'''Network Architecture:''' ResNet-50<br />
<br />
The paper replicated the setup of Goyal et al. (2017) while modifying the number of TPU devices, batch size, learning rate, and then calculating the time to complete 90 epochs, and measuring the accuracy, and performed the following experiments below:<br />
<br />
[[File:Paper_40_Table_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Model training times can be reduced by increasing the batch size during training.<br />
<br />
== RELATED WORK ==<br />
Main related work mentioned in the paper is as follows:<br />
<br />
- Smith & Le (2017) interpreted Stochastic gradient descent as stochastic differential equation; the paper built on this idea to include decaying learning rate.<br />
<br />
- Mandt et al. (2017) analyzed how to modify SGD for the task of Bayesian posterior sampling.<br />
<br />
- Keskar et al. (2016) focused on the analysis of noise once the training is started.<br />
<br />
- Moreover, the proportional relationship between batch size and learning rate was first discovered by Goyal et al. (2017) and successfully trained ResNet-50 on ImageNet in one hour after discovering the proportionality relationship between batch size and learning rate.<br />
<br />
- Furthermore, You et al. (2017a) presented Layer-wise Adaptive Rate Scaling (LARS), which is applying different learning rates to train ImageNet in 14 minutes and 74.9% accuracy. <br />
<br />
- Wilson et al. (2017) argued that adaptive optimization methods tend to generalize less well than SGD and SGD with momentum (although<br />
they did not include K-FAC in their study), while the authors' work reduces the gap in convergence speed.<br />
<br />
- Finally, another strategy called Asynchronous-SGD that allowed (Recht et al., 2011; Dean et al., 2012) to use multiple GPUs even with small batch sizes.<br />
<br />
== CONCLUSIONS ==<br />
Increasing the batch size during training has the same benefits of decaying the learning rate in addition to reducing the number of parameter updates, which corresponds to faster training time. Experiments were performed on different image datasets and various optimizers with different training schedules to prove this result. The paper proposed to increase the learning rate and momentum parameter <math>m</math>, while scaling <math> B \propto \frac{\epsilon}{1-m} </math>, which achieves fewer parameter updates, but slightly less test set accuracy as mentioned in detail in the experiments’ section. In summary, on ImageNet dataset, Inception-ResNet-V2 achieved 77% validation accuracy in under 2500 parameter updates, and ResNet-50 achieved 76.1% validation set accuracy on TPU in less than 30 minutes. One of the great finding of this paper is that all the methods use the hyper-parameters directly from previous works in the literature, and no additional hyper-parameter tuning was performed.<br />
<br />
== CRITIQUE ==<br />
'''Pros:'''<br />
<br />
- The paper showed empirically that increasing batch size and decaying learning rate are equivalent.<br />
<br />
- Several experiments were performed on different optimizers such as SGD and Adam.<br />
<br />
- Had several comparisons with previous experimental setups.<br />
<br />
'''Cons:'''<br />
<br />
<br />
- All datasets used are image datasets. Other experiments should have been done on datasets from different domains to ensure generalization. <br />
<br />
- The number of parameter updates was used as a comparison criterion, but wall-clock times could have provided additional measurable judgment although they depend on the hardware used.<br />
<br />
- Special hardware is needed for large batch training, which is not always feasible. As batch-size increases, we generally need more RAM to train the same model. However, if learning rate is decreased, the RAM use remains constant. As a result, learning rate decay will allow us to train bigger models.<br />
<br />
- In section 5.2 (Increasing the Effective Learning rate), the authors did not test a range of learning rate values and used only (0.1 and 0.5). Additional results from varying the initial learning rate values from 0.1 to 3.2 are provided in the appendix, which indicates that the test accuracy begins to fall for initial learning rates greater than ~0.4. The appended results do not show validation set accuracy curves like in Figure 6, however. It would be beneficial to see if they were similar to the original 0.1 and 0.5 initial learning rate baselines.<br />
<br />
- Although the main idea of the paper is interesting, its results does not seem to be too surprising in comparison with other recent papers in the subject.<br />
<br />
- The paper could benefit from using some other models to demonstrate its claim and generalize its idea by adding some comparisons with other models as well as other recent methods to increase batch size.<br />
<br />
- The paper presents interesting ideas. However, it lacks of mathematical and theoretical analysis beyond the idea. Since the experiment is primary on image dataset and it does not provide sufficient theories, the paper itself presents limited applicability to other types. <br />
<br />
- Also, in experimental setting, only single training runs from one random initialization is used. It would be better to take the best of many runs or to show confidence intervals.<br />
<br />
- It is proposed that we should compare learning rate decay with batch-size increase under the setting that total budget / number of training samples is fixed.<br />
<br />
== REFERENCES ==<br />
- Takuya Akiba, Shuji Suzuki, and Keisuke Fukuda. Extremely large minibatch sgd: Training resnet-50 on imagenet in 15 minutes. arXiv preprint arXiv:1711.04325, 2017.<br />
<br />
- Lukas Balles, Javier Romero, and Philipp Hennig. Coupling adaptive batch sizes with learning rates.arXiv preprint arXiv:1612.05086, 2016.<br />
<br />
- L´eon Bottou, Frank E Curtis, and Jorge Nocedal. Optimization methods for large-scale machine learning.arXiv preprint arXiv:1606.04838, 2016.<br />
<br />
- Richard H Byrd, Gillian M Chin, Jorge Nocedal, and Yuchen Wu. Sample size selection in optimization methods for machine learning. Mathematical programming, 134(1):127–155, 2012.<br />
<br />
- Pratik Chaudhari, Anna Choromanska, Stefano Soatto, and Yann LeCun. Entropy-SGD: Biasing gradient descent into wide valleys. arXiv preprint arXiv:1611.01838, 2016.<br />
<br />
- Soham De, Abhay Yadav, David Jacobs, and Tom Goldstein. Automated inference with adaptive batches. In Artificial Intelligence and Statistics, pp. 1504–1513, 2017.<br />
<br />
- Jeffrey Dean, Greg Corrado, Rajat Monga, Kai Chen, Matthieu Devin, Mark Mao, Andrew Senior, Paul Tucker, Ke Yang, Quoc V Le, et al. Large scale distributed deep networks. In Advances in neural information processing systems, pp. 1223–1231, 2012.<br />
<br />
- Michael P Friedlander and Mark Schmidt. Hybrid deterministic-stochastic methods for data fitting.SIAM Journal on Scientific Computing, 34(3):A1380–A1405, 2012.<br />
<br />
- Priya Goyal, Piotr Doll´ar, Ross Girshick, Pieter Noordhuis, Lukasz Wesolowski, Aapo Kyrola, Andrew Tulloch, Yangqing Jia, and Kaiming He. Accurate, large minibatch SGD: Training imagenet in 1 hour. arXiv preprint arXiv:1706.02677, 2017.<br />
<br />
- Sepp Hochreiter and J¨urgen Schmidhuber. Flat minima. Neural Computation, 9(1):1–42, 1997.<br />
<br />
- Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. arXiv preprint arXiv:1705.08741, 2017.<br />
<br />
- Norman P Jouppi, Cliff Young, Nishant Patil, David Patterson, Gaurav Agrawal, Raminder Bajwa, Sarah Bates, Suresh Bhatia, Nan Boden, Al Borchers, et al. In-datacenter performance analysis of a tensor processing unit. In Proceedings of the 44th Annual International Symposium on Computer Architecture, pp. 1–12. ACM, 2017.<br />
<br />
- Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang. On large-batch training for deep learning: Generalization gap and sharp minima. arXiv preprint arXiv:1609.04836, 2016.<br />
<br />
- Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.<br />
<br />
- Alex Krizhevsky. One weird trick for parallelizing convolutional neural networks. arXiv preprint arXiv:1404.5997, 2014.<br />
<br />
- Qianxiao Li, Cheng Tai, and E Weinan. Stochastic modified equations and adaptive stochastic gradient algorithms. arXiv preprint arXiv:1511.06251, 2017.<br />
<br />
- Ilya Loshchilov and Frank Hutter. SGDR: stochastic gradient descent with restarts. arXiv preprint arXiv:1608.03983, 2016.<br />
<br />
- Stephan Mandt, Matthew D Hoffman, and DavidMBlei. Stochastic gradient descent as approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.<br />
<br />
- James Martens and Roger Grosse. Optimizing neural networks with kronecker-factored approximate curvature. In International Conference on Machine Learning, pp. 2408–2417, 2015.<br />
<br />
- Yurii Nesterov. A method of solving a convex programming problem with convergence rate o (1/k2). In Soviet Mathematics Doklady, volume 27, pp. 372–376, 1983.<br />
<br />
- Lutz Prechelt. Early stopping-but when? Neural Networks: Tricks of the trade, pp. 553–553, 1998.<br />
<br />
- Benjamin Recht, Christopher Re, Stephen Wright, and Feng Niu. Hogwild: A lock-free approach to parallelizing stochastic gradient descent. In Advances in neural information processing systems, pp. 693–701, 2011.<br />
<br />
- Herbert Robbins and Sutton Monro. A stochastic approximation method. The annals of mathematical statistics, pp. 400–407, 1951.<br />
<br />
- Samuel L. Smith and Quoc V. Le. A bayesian perspective on generalization and stochastic gradient descent. arXiv preprint arXiv:1710.06451, 2017.<br />
<br />
- Christian Szegedy, Sergey Ioffe, Vincent Vanhoucke, and Alexander A Alemi. Inception-v4, Inception-ResNet and the impact of residual connections on learning. In AAAI, pp. 4278–4284, 2017.<br />
<br />
- Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics. In Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 681–688, 2011.<br />
<br />
- Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
- Yang You, Igor Gitman, and Boris Ginsburg. Scaling SGD batch size to 32k for imagenet training. arXiv preprint arXiv:1708.03888, 2017a.<br />
<br />
- Yang You, Zhao Zhang, C Hsieh, James Demmel, and Kurt Keutzer. Imagenet training in minutes. CoRR, abs/1709.05011, 2017b.<br />
<br />
- Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. arXiv preprint arXiv:1605.07146, 2016.<br />
<br />
- Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DON%27T_DECAY_THE_LEARNING_RATE_,_INCREASE_THE_BATCH_SIZE&diff=42031DON'T DECAY THE LEARNING RATE , INCREASE THE BATCH SIZE2018-11-30T11:02:34Z<p>A22ravi: /* CONCLUSIONS */</p>
<hr />
<div>Summary of the ICLR 2018 paper: '''Don't Decay the learning Rate, Increase the Batch Size ''' <br />
<br />
Link: [https://arxiv.org/pdf/1711.00489.pdf]<br />
<br />
Summarized by: Afify, Ahmed [ID: 20700841]<br />
<br />
==INTUITION==<br />
Nowadays, it is a common practice not to have a singular steady learning rate for the learning phase of neural network models. Instead, we use adaptive learning rates with the standard gradient descent method. The intuition behind this is that when we are far away from the minima, it is beneficial for us to take large steps towards the minima, as it would require a lesser number of steps to converge, but as we approach the minima, our step size should decrease, otherwise we may just keep oscillating around the minima. In practice, this is generally achieved by methods like SGD with momentum, Nesterov momentum, and Adam. However, the core claim of this paper is that the same effect can be achieved by increasing the batch size during the gradient descent process while keeping the learning rate constant throughout. In addition, the paper argues that such an approach also reduces the parameter updates required to reach the minima, thus leading to greater parallelism and shorter training times.<br />
<br />
== INTRODUCTION ==<br />
Stochastic gradient descent (SGD) is the most widely used optimization technique for training deep learning models. The reason for this is that the minima found using this process generalizes well (Zhang et al., 2016; Wilson et al., 2017), but the optimization process is slow and time consuming. According to (Goyal et al., 2017; Hoffer et al., 2017; You et al., 2017a), this has motivated researchers to try to speed up this optimization process by taking bigger steps, and hence reduce the number of parameter updates in training a model. This can be achieved by using large batch training, which can be divided across many machines. <br />
<br />
However, increasing the batch size leads to decreasing the test set accuracy (Keskar et al., 2016; Goyal et al., 2017). Smith and Le (2017) believed that SGD has a scale of random fluctuations <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N number of training samples, and B batch size. They concluded that there is an optimal batch size proportional to the learning rate when <math> B \ll N </math>, and optimum fluctuation scale <math>g</math> for a maximum test set accuracy.<br />
<br />
In this paper, the authors' main goal is to provide evidence that increasing the batch size is quantitatively equivalent to decreasing the learning rate with the same number of training epochs in decreasing the scale of random fluctuations, but with remarkably less number of parameter updates. Moreover, an additional reduction in the number of parameter updates can be attained by increasing the learning rate and scaling <math> B \propto \epsilon </math> or even more reduction by increasing the momentum coefficient and scaling <math> B \propto \frac{1}{1-m} </math> although the latter decreases the test accuracy. This has been demonstrated by several experiments on the ImageNet and CIFAR-10 datasets using ResNet-50 and Inception-ResNet-V2 architectures respectively.<br />
<br />
== STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION ==<br />
As mentioned in the previous section, the drawback of SGD when compared to full-batch training is the noise that it introduces that hinders optimization. According to (Robbins & Monro, 1951), there are two equations that govern how to reach the minimum of a convex function: (<math> \epsilon_i </math> denotes the learning rate at the <math> i^{th} </math> gradient update)<br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon_i = \infty </math>. This equation guarantees that we will reach the minimum. <br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon^2_i < \infty </math>. This equation, which is valid only for a fixed batch size, guarantees that learning rate decays fast enough allowing us to reach the minimum rather than bouncing due to noise.<br />
<br />
These equations indicate that the learning rate must decay during training, and second equation is only available when the batch size is constant. To change the batch size, Smith and Le (2017) proposed to interpret SGD as integrating this stochastic differential equation <math> \frac{dw}{dt} = -\frac{dC}{dw} + \eta(t) </math>, where <math>C</math> represents cost function, <math>w</math> represents the parameters, and <math>\eta</math> represents the Gaussian random noise. Furthermore, they proved that noise scale <math>g</math> controls the magnitude of random fluctuations in the training dynamics by this formula: <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N is the training set size and <math>B</math> is the batch size. As we usually have <math> B \ll N </math>, we can define <math> g \approx \epsilon \frac{N}{B} </math>. This explains why when the learning rate decreases, noise <math>g</math> decreases, enabling us to converge to the minimum of the cost function. However, increasing the batch size has the same effect and makes <math>g</math> decays with constant learning rate. In this work, the batch size is increased until <math> B \approx \frac{N}{10} </math>, then the conventional way of decaying the learning rate is followed.<br />
<br />
== SIMULATED ANNEALING AND THE GENERALIZATION GAP ==<br />
'''Simulated Annealing:''' decaying learning rates are empirically successful. To understand this, they note that introducing random fluctuations<br />
whose scale falls during training is also a well established technique in non-convex optimization; simulated annealing. The initial noisy optimization phase allows to explore a larger fraction of the parameter space without becoming trapped in local minima. Once a promising region of parameter space is located, the noise is reduced to fine-tune the parameters.<br />
<br />
For more info: Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as gradient descent. [https://en.wikipedia.org/wiki/Simulated_annealing [Reference]]<br />
<br />
'''Generalization Gap:''' Small batch data generalizes better to the test set than large batch data.<br />
<br />
Smith and Le (2017) found that there is an optimal batch size which corresponds to optimal noise scale g <math> (g \approx \epsilon \frac{N}{B}) </math> and concluded that <math> B_{opt} \propto \epsilon N </math> that corresponds to maximum test set accuracy. This means that gradient noise is helpful as it makes SGD escape sharp minima, which does not generalize well. <br />
<br />
Simulated Annealing is a famous technique in non-convex optimization. Starting with noise in the training process helps us to discover a wide range of parameters then once we are near the optimum value, noise is reduced to fine tune our final parameters. However, more and more researches like to use the sharper decay schedules like cosine decay or step-function drops. In physical sciences, slowly annealing (or decaying) the temperature (which is the noise scale in this situation) helps to converge to the global minimum, which is sharp. But decaying the temperature in discrete steps can make the system stuck in a local minimum, which lead to higher cost and lower curvature. The authors think that deep learning has the same intuition.<br />
.<br />
<br />
== THE EFFECTIVE LEARNING RATE AND THE ACCUMULATION VARIABLE ==<br />
'''The Effective Learning Rate''' : <math> \epsilon_{eff} = \frac{\epsilon}{1-m} </math><br />
<br />
Smith and Le (2017) included momentum to the equation of the vanilla SGD noise scale that was defined above to be: <math> g = \frac{\epsilon}{1-m}(\frac{N}{B}-1)\approx \frac{\epsilon N}{B(1-m)} </math>, which is the same as the previous equation when m goes to 0. They found that increasing the learning rate and momentum coefficient and scaling <math> B \propto \frac{\epsilon }{1-m} </math> reduces the number of parameter updates, but the test accuracy decreases when the momentum coefficient is increased. <br />
<br />
To understand the reasons behind this, we need to analyze momentum update equations below:<br />
<br />
<center><math><br />
\Delta A = -(1-m)A + \frac{d\widehat{C}}{dw} <br />
</math><br />
<br />
<math><br />
\Delta w = -A\epsilon<br />
</math><br />
</center><br />
<br />
We can see that the Accumulation variable A, which is initially set to 0, then increases exponentially to reach its steady state value during <math> \frac{B}{N(1-m)} </math> training epochs while <math> \Delta w </math> is suppressed that can reduce the rate of convergence. Moreover, at high momentum, we have three challenges:<br />
<br />
1- Additional epochs are needed to catch up with the accumulation.<br />
<br />
2- Accumulation needs more time <math> \frac{B}{N(1-m)} </math> to forget old gradients. <br />
<br />
3- After this time, however, the accumulation cannot adapt to changes in the loss landscape.<br />
<br />
4- In the early stage, large batch size will lead to the instabilities.<br />
<br />
== EXPERIMENTS ==<br />
=== SIMULATED ANNEALING IN A WIDE RESNET ===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Schedules used as in the below figure:''' <br />
<br />
- Decaying learning rate: learning rate decays by a factor of 5 at a sequence of “steps”, and the batch size is constant<br />
<br />
- Increasing batch size: learning rate is constant, and the batch size is increased by a factor of 5 at every step.<br />
<br />
- Hybrid: At the beginning, the learning rate is constant and batch size is increased by a factor of 5. Then, the learning rate decays by a factor of 5 at each subsequent step, and the batch size is constant. This is the schedule that will be used if there is a hardware limit affecting a maximum batch size limit.<br />
<br />
[[File:Paper_40_Fig_1.png | 800px|center]]<br />
<br />
As shown in the below figure: in the left figure (2a), we can observe that for the training set, the three learning curves are exactly the same while in figure 2b, increasing the batch size has a huge advantage of reducing the number of parameter updates.<br />
This concludes that noise scale is the one that needs to be decayed and not the learning rate itself<br />
[[File:Paper_40_Fig_2.png | 800px|center]] <br />
<br />
To make sure that these results are the same for the test set as well, in figure 3, we can see that the three learning curves are exactly the same for SGD with momentum, and Nesterov momentum<br />
[[File:Paper_40_Fig_3.png | 800px|center]]<br />
<br />
To check for other optimizers as well. the below figure shows the same experiment as in figure 3, which is the three learning curves for test set, but for vanilla SGD and Adam, and showing <br />
[[File:Paper_40_Fig_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Decreasing the learning rate and increasing the batch size during training are equivalent<br />
<br />
=== INCREASING THE EFFECTIVE LEARNING RATE===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Parameters:''' Optimization Algorithm: SGD with momentum / Maximum batch size = 5120<br />
<br />
'''Training Schedules:''' <br />
<br />
The authors consider four training schedules, all of which decay the noise scale by a factor of five in a series of three steps with the same number of epochs.<br />
<br />
Original training schedule: initial learning rate of 0.1 which decays by a factor of 5 at each step, a momentum coefficient of 0.9, and a batch size of 128. <br />
<br />
Increasing batch size: learning rate of 0.1, momentum coefficient of 0.9, initial batch size of 128 that increases by a factor of 5 at each step. <br />
<br />
Increased initial learning rate: initial learning rate of 0.5, initial batch size of 640 that increase during training.<br />
<br />
Increased momentum coefficient: increased initial learning rate of 0.5, initial batch size of 3200 that increase during training, and an increased momentum coefficient of 0.98.<br />
<br />
The results of all training schedules, which are presented in the below figure, are documented in the following table:<br />
<br />
[[File:Paper_40_Table_1.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_5.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the effective learning rate and scaling the batch size results in further reduction in the number of parameter updates<br />
<br />
=== TRAINING IMAGENET IN 2500 PARAMETER UPDATES===<br />
<br />
'''A) Experiment Goal:''' Control Batch Size<br />
<br />
'''Dataset:''' ImageNet (1.28 million training images)<br />
<br />
The paper modified the setup of Goyal et al. (2017), and used the following configuration:<br />
<br />
'''Network Architecture:''' Inception-ResNet-V2 <br />
<br />
'''Training Parameters:''' <br />
<br />
90 epochs / noise decayed at epoch 30, 60, and 80 by a factor of 10 / Initial ghost batch size = 32 / Learning rate = 3 / momentum coefficient = 0.9 / Initial batch size = 8192<br />
<br />
Two training schedules were used:<br />
<br />
“Decaying learning rate”, where batch size is fixed and the learning rate is decayed<br />
<br />
“Increasing batch size”, where batch size is increased to 81920 then the learning rate is decayed at two steps.<br />
<br />
[[File:Paper_40_Table_2.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_6.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the batch size resulted in reducing the number of parameter updates from 14,000 to 6,000.<br />
<br />
'''B) Experiment Goal:''' Control Batch Size and Momentum Coefficient<br />
<br />
'''Training Parameters:''' Ghost batch size = 64 / noise decayed at epoch 30, 60, and 80 by a factor of 10. <br />
<br />
The below table shows the number of parameter updates and accuracy for different set of training parameters:<br />
<br />
[[File:Paper_40_Table_3.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_7.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the momentum reduces the number of parameter updates, but leads to a drop in the test accuracy.<br />
<br />
=== TRAINING IMAGENET IN 30 MINUTES===<br />
<br />
'''Dataset:''' ImageNet (Already introduced in the previous section)<br />
<br />
'''Network Architecture:''' ResNet-50<br />
<br />
The paper replicated the setup of Goyal et al. (2017) while modifying the number of TPU devices, batch size, learning rate, and then calculating the time to complete 90 epochs, and measuring the accuracy, and performed the following experiments below:<br />
<br />
[[File:Paper_40_Table_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Model training times can be reduced by increasing the batch size during training.<br />
<br />
== RELATED WORK ==<br />
Main related work mentioned in the paper is as follows:<br />
<br />
- Smith & Le (2017) interpreted Stochastic gradient descent as stochastic differential equation; the paper built on this idea to include decaying learning rate.<br />
<br />
- Mandt et al. (2017) analyzed how to modify SGD for the task of Bayesian posterior sampling.<br />
<br />
- Keskar et al. (2016) focused on the analysis of noise once the training is started.<br />
<br />
- Moreover, the proportional relationship between batch size and learning rate was first discovered by Goyal et al. (2017) and successfully trained ResNet-50 on ImageNet in one hour after discovering the proportionality relationship between batch size and learning rate.<br />
<br />
- Furthermore, You et al. (2017a) presented Layer-wise Adaptive Rate Scaling (LARS), which is applying different learning rates to train ImageNet in 14 minutes and 74.9% accuracy. <br />
<br />
- Wilson et al. (2017) argued that adaptive optimization methods tend to generalize less well than SGD and SGD with momentum (although<br />
they did not include K-FAC in their study), while the authors' work reduces the gap in convergence speed.<br />
<br />
- Finally, another strategy called Asynchronous-SGD that allowed (Recht et al., 2011; Dean et al., 2012) to use multiple GPUs even with small batch sizes.<br />
<br />
== CONCLUSIONS ==<br />
Increasing batch size during training has the same benefits of decaying the learning rate in addition to reducing the number of parameter updates, which corresponds to faster training time. Experiments were performed on different image datasets and various optimizers with different training schedules to prove this result. The paper proposed to increase the learning rate and momentum parameter <math>m</math>, while scaling <math> B \propto \frac{\epsilon}{1-m} </math>, which achieves fewer parameter updates, but slightly less test set accuracy as mentioned in detail in the experiments’ section. In summary, on ImageNet dataset, Inception-ResNet-V2 achieved 77% validation accuracy in under 2500 parameter updates, and ResNet-50 achieved 76.1% validation set accuracy on TPU in less than 30 minutes. One of the great findings of this paper is that the methods use the hyper-parameters directly from previous works in the literature, and no additional hyper parameter tuning was performed.<br />
<br />
== CRITIQUE ==<br />
'''Pros:'''<br />
<br />
- The paper showed empirically that increasing batch size and decaying learning rate are equivalent.<br />
<br />
- Several experiments were performed on different optimizers such as SGD and Adam.<br />
<br />
- Had several comparisons with previous experimental setups.<br />
<br />
'''Cons:'''<br />
<br />
<br />
- All datasets used are image datasets. Other experiments should have been done on datasets from different domains to ensure generalization. <br />
<br />
- The number of parameter updates was used as a comparison criterion, but wall-clock times could have provided additional measurable judgment although they depend on the hardware used.<br />
<br />
- Special hardware is needed for large batch training, which is not always feasible. As batch-size increases, we generally need more RAM to train the same model. However, if learning rate is decreased, the RAM use remains constant. As a result, learning rate decay will allow us to train bigger models.<br />
<br />
- In section 5.2 (Increasing the Effective Learning rate), the authors did not test a range of learning rate values and used only (0.1 and 0.5). Additional results from varying the initial learning rate values from 0.1 to 3.2 are provided in the appendix, which indicates that the test accuracy begins to fall for initial learning rates greater than ~0.4. The appended results do not show validation set accuracy curves like in Figure 6, however. It would be beneficial to see if they were similar to the original 0.1 and 0.5 initial learning rate baselines.<br />
<br />
- Although the main idea of the paper is interesting, its results does not seem to be too surprising in comparison with other recent papers in the subject.<br />
<br />
- The paper could benefit from using some other models to demonstrate its claim and generalize its idea by adding some comparisons with other models as well as other recent methods to increase batch size.<br />
<br />
- The paper presents interesting ideas. However, it lacks of mathematical and theoretical analysis beyond the idea. Since the experiment is primary on image dataset and it does not provide sufficient theories, the paper itself presents limited applicability to other types. <br />
<br />
- Also, in experimental setting, only single training runs from one random initialization is used. It would be better to take the best of many runs or to show confidence intervals.<br />
<br />
- It is proposed that we should compare learning rate decay with batch-size increase under the setting that total budget / number of training samples is fixed.<br />
<br />
== REFERENCES ==<br />
- Takuya Akiba, Shuji Suzuki, and Keisuke Fukuda. Extremely large minibatch sgd: Training resnet-50 on imagenet in 15 minutes. arXiv preprint arXiv:1711.04325, 2017.<br />
<br />
- Lukas Balles, Javier Romero, and Philipp Hennig. Coupling adaptive batch sizes with learning rates.arXiv preprint arXiv:1612.05086, 2016.<br />
<br />
- L´eon Bottou, Frank E Curtis, and Jorge Nocedal. Optimization methods for large-scale machine learning.arXiv preprint arXiv:1606.04838, 2016.<br />
<br />
- Richard H Byrd, Gillian M Chin, Jorge Nocedal, and Yuchen Wu. Sample size selection in optimization methods for machine learning. Mathematical programming, 134(1):127–155, 2012.<br />
<br />
- Pratik Chaudhari, Anna Choromanska, Stefano Soatto, and Yann LeCun. Entropy-SGD: Biasing gradient descent into wide valleys. arXiv preprint arXiv:1611.01838, 2016.<br />
<br />
- Soham De, Abhay Yadav, David Jacobs, and Tom Goldstein. Automated inference with adaptive batches. In Artificial Intelligence and Statistics, pp. 1504–1513, 2017.<br />
<br />
- Jeffrey Dean, Greg Corrado, Rajat Monga, Kai Chen, Matthieu Devin, Mark Mao, Andrew Senior, Paul Tucker, Ke Yang, Quoc V Le, et al. Large scale distributed deep networks. In Advances in neural information processing systems, pp. 1223–1231, 2012.<br />
<br />
- Michael P Friedlander and Mark Schmidt. Hybrid deterministic-stochastic methods for data fitting.SIAM Journal on Scientific Computing, 34(3):A1380–A1405, 2012.<br />
<br />
- Priya Goyal, Piotr Doll´ar, Ross Girshick, Pieter Noordhuis, Lukasz Wesolowski, Aapo Kyrola, Andrew Tulloch, Yangqing Jia, and Kaiming He. Accurate, large minibatch SGD: Training imagenet in 1 hour. arXiv preprint arXiv:1706.02677, 2017.<br />
<br />
- Sepp Hochreiter and J¨urgen Schmidhuber. Flat minima. Neural Computation, 9(1):1–42, 1997.<br />
<br />
- Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. arXiv preprint arXiv:1705.08741, 2017.<br />
<br />
- Norman P Jouppi, Cliff Young, Nishant Patil, David Patterson, Gaurav Agrawal, Raminder Bajwa, Sarah Bates, Suresh Bhatia, Nan Boden, Al Borchers, et al. In-datacenter performance analysis of a tensor processing unit. In Proceedings of the 44th Annual International Symposium on Computer Architecture, pp. 1–12. ACM, 2017.<br />
<br />
- Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang. On large-batch training for deep learning: Generalization gap and sharp minima. arXiv preprint arXiv:1609.04836, 2016.<br />
<br />
- Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.<br />
<br />
- Alex Krizhevsky. One weird trick for parallelizing convolutional neural networks. arXiv preprint arXiv:1404.5997, 2014.<br />
<br />
- Qianxiao Li, Cheng Tai, and E Weinan. Stochastic modified equations and adaptive stochastic gradient algorithms. arXiv preprint arXiv:1511.06251, 2017.<br />
<br />
- Ilya Loshchilov and Frank Hutter. SGDR: stochastic gradient descent with restarts. arXiv preprint arXiv:1608.03983, 2016.<br />
<br />
- Stephan Mandt, Matthew D Hoffman, and DavidMBlei. Stochastic gradient descent as approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.<br />
<br />
- James Martens and Roger Grosse. Optimizing neural networks with kronecker-factored approximate curvature. In International Conference on Machine Learning, pp. 2408–2417, 2015.<br />
<br />
- Yurii Nesterov. A method of solving a convex programming problem with convergence rate o (1/k2). In Soviet Mathematics Doklady, volume 27, pp. 372–376, 1983.<br />
<br />
- Lutz Prechelt. Early stopping-but when? Neural Networks: Tricks of the trade, pp. 553–553, 1998.<br />
<br />
- Benjamin Recht, Christopher Re, Stephen Wright, and Feng Niu. Hogwild: A lock-free approach to parallelizing stochastic gradient descent. In Advances in neural information processing systems, pp. 693–701, 2011.<br />
<br />
- Herbert Robbins and Sutton Monro. A stochastic approximation method. The annals of mathematical statistics, pp. 400–407, 1951.<br />
<br />
- Samuel L. Smith and Quoc V. Le. A bayesian perspective on generalization and stochastic gradient descent. arXiv preprint arXiv:1710.06451, 2017.<br />
<br />
- Christian Szegedy, Sergey Ioffe, Vincent Vanhoucke, and Alexander A Alemi. Inception-v4, Inception-ResNet and the impact of residual connections on learning. In AAAI, pp. 4278–4284, 2017.<br />
<br />
- Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics. In Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 681–688, 2011.<br />
<br />
- Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
- Yang You, Igor Gitman, and Boris Ginsburg. Scaling SGD batch size to 32k for imagenet training. arXiv preprint arXiv:1708.03888, 2017a.<br />
<br />
- Yang You, Zhao Zhang, C Hsieh, James Demmel, and Kurt Keutzer. Imagenet training in minutes. CoRR, abs/1709.05011, 2017b.<br />
<br />
- Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. arXiv preprint arXiv:1605.07146, 2016.<br />
<br />
- Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DON%27T_DECAY_THE_LEARNING_RATE_,_INCREASE_THE_BATCH_SIZE&diff=42030DON'T DECAY THE LEARNING RATE , INCREASE THE BATCH SIZE2018-11-30T10:56:12Z<p>A22ravi: /* STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION */</p>
<hr />
<div>Summary of the ICLR 2018 paper: '''Don't Decay the learning Rate, Increase the Batch Size ''' <br />
<br />
Link: [https://arxiv.org/pdf/1711.00489.pdf]<br />
<br />
Summarized by: Afify, Ahmed [ID: 20700841]<br />
<br />
==INTUITION==<br />
Nowadays, it is a common practice not to have a singular steady learning rate for the learning phase of neural network models. Instead, we use adaptive learning rates with the standard gradient descent method. The intuition behind this is that when we are far away from the minima, it is beneficial for us to take large steps towards the minima, as it would require a lesser number of steps to converge, but as we approach the minima, our step size should decrease, otherwise we may just keep oscillating around the minima. In practice, this is generally achieved by methods like SGD with momentum, Nesterov momentum, and Adam. However, the core claim of this paper is that the same effect can be achieved by increasing the batch size during the gradient descent process while keeping the learning rate constant throughout. In addition, the paper argues that such an approach also reduces the parameter updates required to reach the minima, thus leading to greater parallelism and shorter training times.<br />
<br />
== INTRODUCTION ==<br />
Stochastic gradient descent (SGD) is the most widely used optimization technique for training deep learning models. The reason for this is that the minima found using this process generalizes well (Zhang et al., 2016; Wilson et al., 2017), but the optimization process is slow and time consuming. According to (Goyal et al., 2017; Hoffer et al., 2017; You et al., 2017a), this has motivated researchers to try to speed up this optimization process by taking bigger steps, and hence reduce the number of parameter updates in training a model. This can be achieved by using large batch training, which can be divided across many machines. <br />
<br />
However, increasing the batch size leads to decreasing the test set accuracy (Keskar et al., 2016; Goyal et al., 2017). Smith and Le (2017) believed that SGD has a scale of random fluctuations <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N number of training samples, and B batch size. They concluded that there is an optimal batch size proportional to the learning rate when <math> B \ll N </math>, and optimum fluctuation scale <math>g</math> for a maximum test set accuracy.<br />
<br />
In this paper, the authors' main goal is to provide evidence that increasing the batch size is quantitatively equivalent to decreasing the learning rate with the same number of training epochs in decreasing the scale of random fluctuations, but with remarkably less number of parameter updates. Moreover, an additional reduction in the number of parameter updates can be attained by increasing the learning rate and scaling <math> B \propto \epsilon </math> or even more reduction by increasing the momentum coefficient and scaling <math> B \propto \frac{1}{1-m} </math> although the latter decreases the test accuracy. This has been demonstrated by several experiments on the ImageNet and CIFAR-10 datasets using ResNet-50 and Inception-ResNet-V2 architectures respectively.<br />
<br />
== STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION ==<br />
As mentioned in the previous section, the drawback of SGD when compared to full-batch training is the noise that it introduces that hinders optimization. According to (Robbins & Monro, 1951), there are two equations that govern how to reach the minimum of a convex function: (<math> \epsilon_i </math> denotes the learning rate at the <math> i^{th} </math> gradient update)<br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon_i = \infty </math>. This equation guarantees that we will reach the minimum. <br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon^2_i < \infty </math>. This equation, which is valid only for a fixed batch size, guarantees that learning rate decays fast enough allowing us to reach the minimum rather than bouncing due to noise.<br />
<br />
These equations indicate that the learning rate must decay during training, and second equation is only available when the batch size is constant. To change the batch size, Smith and Le (2017) proposed to interpret SGD as integrating this stochastic differential equation <math> \frac{dw}{dt} = -\frac{dC}{dw} + \eta(t) </math>, where <math>C</math> represents cost function, <math>w</math> represents the parameters, and <math>\eta</math> represents the Gaussian random noise. Furthermore, they proved that noise scale <math>g</math> controls the magnitude of random fluctuations in the training dynamics by this formula: <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N is the training set size and <math>B</math> is the batch size. As we usually have <math> B \ll N </math>, we can define <math> g \approx \epsilon \frac{N}{B} </math>. This explains why when the learning rate decreases, noise <math>g</math> decreases, enabling us to converge to the minimum of the cost function. However, increasing the batch size has the same effect and makes <math>g</math> decays with constant learning rate. In this work, the batch size is increased until <math> B \approx \frac{N}{10} </math>, then the conventional way of decaying the learning rate is followed.<br />
<br />
== SIMULATED ANNEALING AND THE GENERALIZATION GAP ==<br />
'''Simulated Annealing:''' decaying learning rates are empirically successful. To understand this, they note that introducing random fluctuations<br />
whose scale falls during training is also a well established technique in non-convex optimization; simulated annealing. The initial noisy optimization phase allows to explore a larger fraction of the parameter space without becoming trapped in local minima. Once a promising region of parameter space is located, the noise is reduced to fine-tune the parameters.<br />
<br />
For more info: Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as gradient descent. [https://en.wikipedia.org/wiki/Simulated_annealing [Reference]]<br />
<br />
'''Generalization Gap:''' Small batch data generalizes better to the test set than large batch data.<br />
<br />
Smith and Le (2017) found that there is an optimal batch size which corresponds to optimal noise scale g <math> (g \approx \epsilon \frac{N}{B}) </math> and concluded that <math> B_{opt} \propto \epsilon N </math> that corresponds to maximum test set accuracy. This means that gradient noise is helpful as it makes SGD escape sharp minima, which does not generalize well. <br />
<br />
Simulated Annealing is a famous technique in non-convex optimization. Starting with noise in the training process helps us to discover a wide range of parameters then once we are near the optimum value, noise is reduced to fine tune our final parameters. However, more and more researches like to use the sharper decay schedules like cosine decay or step-function drops. In physical sciences, slowly annealing (or decaying) the temperature (which is the noise scale in this situation) helps to converge to the global minimum, which is sharp. But decaying the temperature in discrete steps can make the system stuck in a local minimum, which lead to higher cost and lower curvature. The authors think that deep learning has the same intuition.<br />
.<br />
<br />
== THE EFFECTIVE LEARNING RATE AND THE ACCUMULATION VARIABLE ==<br />
'''The Effective Learning Rate''' : <math> \epsilon_{eff} = \frac{\epsilon}{1-m} </math><br />
<br />
Smith and Le (2017) included momentum to the equation of the vanilla SGD noise scale that was defined above to be: <math> g = \frac{\epsilon}{1-m}(\frac{N}{B}-1)\approx \frac{\epsilon N}{B(1-m)} </math>, which is the same as the previous equation when m goes to 0. They found that increasing the learning rate and momentum coefficient and scaling <math> B \propto \frac{\epsilon }{1-m} </math> reduces the number of parameter updates, but the test accuracy decreases when the momentum coefficient is increased. <br />
<br />
To understand the reasons behind this, we need to analyze momentum update equations below:<br />
<br />
<center><math><br />
\Delta A = -(1-m)A + \frac{d\widehat{C}}{dw} <br />
</math><br />
<br />
<math><br />
\Delta w = -A\epsilon<br />
</math><br />
</center><br />
<br />
We can see that the Accumulation variable A, which is initially set to 0, then increases exponentially to reach its steady state value during <math> \frac{B}{N(1-m)} </math> training epochs while <math> \Delta w </math> is suppressed that can reduce the rate of convergence. Moreover, at high momentum, we have three challenges:<br />
<br />
1- Additional epochs are needed to catch up with the accumulation.<br />
<br />
2- Accumulation needs more time <math> \frac{B}{N(1-m)} </math> to forget old gradients. <br />
<br />
3- After this time, however, the accumulation cannot adapt to changes in the loss landscape.<br />
<br />
4- In the early stage, large batch size will lead to the instabilities.<br />
<br />
== EXPERIMENTS ==<br />
=== SIMULATED ANNEALING IN A WIDE RESNET ===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Schedules used as in the below figure:''' <br />
<br />
- Decaying learning rate: learning rate decays by a factor of 5 at a sequence of “steps”, and the batch size is constant<br />
<br />
- Increasing batch size: learning rate is constant, and the batch size is increased by a factor of 5 at every step.<br />
<br />
- Hybrid: At the beginning, the learning rate is constant and batch size is increased by a factor of 5. Then, the learning rate decays by a factor of 5 at each subsequent step, and the batch size is constant. This is the schedule that will be used if there is a hardware limit affecting a maximum batch size limit.<br />
<br />
[[File:Paper_40_Fig_1.png | 800px|center]]<br />
<br />
As shown in the below figure: in the left figure (2a), we can observe that for the training set, the three learning curves are exactly the same while in figure 2b, increasing the batch size has a huge advantage of reducing the number of parameter updates.<br />
This concludes that noise scale is the one that needs to be decayed and not the learning rate itself<br />
[[File:Paper_40_Fig_2.png | 800px|center]] <br />
<br />
To make sure that these results are the same for the test set as well, in figure 3, we can see that the three learning curves are exactly the same for SGD with momentum, and Nesterov momentum<br />
[[File:Paper_40_Fig_3.png | 800px|center]]<br />
<br />
To check for other optimizers as well. the below figure shows the same experiment as in figure 3, which is the three learning curves for test set, but for vanilla SGD and Adam, and showing <br />
[[File:Paper_40_Fig_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Decreasing the learning rate and increasing the batch size during training are equivalent<br />
<br />
=== INCREASING THE EFFECTIVE LEARNING RATE===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Parameters:''' Optimization Algorithm: SGD with momentum / Maximum batch size = 5120<br />
<br />
'''Training Schedules:''' <br />
<br />
The authors consider four training schedules, all of which decay the noise scale by a factor of five in a series of three steps with the same number of epochs.<br />
<br />
Original training schedule: initial learning rate of 0.1 which decays by a factor of 5 at each step, a momentum coefficient of 0.9, and a batch size of 128. <br />
<br />
Increasing batch size: learning rate of 0.1, momentum coefficient of 0.9, initial batch size of 128 that increases by a factor of 5 at each step. <br />
<br />
Increased initial learning rate: initial learning rate of 0.5, initial batch size of 640 that increase during training.<br />
<br />
Increased momentum coefficient: increased initial learning rate of 0.5, initial batch size of 3200 that increase during training, and an increased momentum coefficient of 0.98.<br />
<br />
The results of all training schedules, which are presented in the below figure, are documented in the following table:<br />
<br />
[[File:Paper_40_Table_1.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_5.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the effective learning rate and scaling the batch size results in further reduction in the number of parameter updates<br />
<br />
=== TRAINING IMAGENET IN 2500 PARAMETER UPDATES===<br />
<br />
'''A) Experiment Goal:''' Control Batch Size<br />
<br />
'''Dataset:''' ImageNet (1.28 million training images)<br />
<br />
The paper modified the setup of Goyal et al. (2017), and used the following configuration:<br />
<br />
'''Network Architecture:''' Inception-ResNet-V2 <br />
<br />
'''Training Parameters:''' <br />
<br />
90 epochs / noise decayed at epoch 30, 60, and 80 by a factor of 10 / Initial ghost batch size = 32 / Learning rate = 3 / momentum coefficient = 0.9 / Initial batch size = 8192<br />
<br />
Two training schedules were used:<br />
<br />
“Decaying learning rate”, where batch size is fixed and the learning rate is decayed<br />
<br />
“Increasing batch size”, where batch size is increased to 81920 then the learning rate is decayed at two steps.<br />
<br />
[[File:Paper_40_Table_2.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_6.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the batch size resulted in reducing the number of parameter updates from 14,000 to 6,000.<br />
<br />
'''B) Experiment Goal:''' Control Batch Size and Momentum Coefficient<br />
<br />
'''Training Parameters:''' Ghost batch size = 64 / noise decayed at epoch 30, 60, and 80 by a factor of 10. <br />
<br />
The below table shows the number of parameter updates and accuracy for different set of training parameters:<br />
<br />
[[File:Paper_40_Table_3.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_7.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the momentum reduces the number of parameter updates, but leads to a drop in the test accuracy.<br />
<br />
=== TRAINING IMAGENET IN 30 MINUTES===<br />
<br />
'''Dataset:''' ImageNet (Already introduced in the previous section)<br />
<br />
'''Network Architecture:''' ResNet-50<br />
<br />
The paper replicated the setup of Goyal et al. (2017) while modifying the number of TPU devices, batch size, learning rate, and then calculating the time to complete 90 epochs, and measuring the accuracy, and performed the following experiments below:<br />
<br />
[[File:Paper_40_Table_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Model training times can be reduced by increasing the batch size during training.<br />
<br />
== RELATED WORK ==<br />
Main related work mentioned in the paper is as follows:<br />
<br />
- Smith & Le (2017) interpreted Stochastic gradient descent as stochastic differential equation; the paper built on this idea to include decaying learning rate.<br />
<br />
- Mandt et al. (2017) analyzed how to modify SGD for the task of Bayesian posterior sampling.<br />
<br />
- Keskar et al. (2016) focused on the analysis of noise once the training is started.<br />
<br />
- Moreover, the proportional relationship between batch size and learning rate was first discovered by Goyal et al. (2017) and successfully trained ResNet-50 on ImageNet in one hour after discovering the proportionality relationship between batch size and learning rate.<br />
<br />
- Furthermore, You et al. (2017a) presented Layer-wise Adaptive Rate Scaling (LARS), which is applying different learning rates to train ImageNet in 14 minutes and 74.9% accuracy. <br />
<br />
- Wilson et al. (2017) argued that adaptive optimization methods tend to generalize less well than SGD and SGD with momentum (although<br />
they did not include K-FAC in their study), while the authors' work reduces the gap in convergence speed.<br />
<br />
- Finally, another strategy called Asynchronous-SGD that allowed (Recht et al., 2011; Dean et al., 2012) to use multiple GPUs even with small batch sizes.<br />
<br />
== CONCLUSIONS ==<br />
Increasing batch size during training has the same benefits of decaying the learning rate in addition to reducing the number of parameter updates, which corresponds to faster training time. Experiments were performed on different image datasets and various optimizers with different training schedules to prove this result. The paper proposed to increase increase the learning rate and momentum parameter <math>m</math>, while scaling <math> B \propto \frac{\epsilon}{1-m} </math>, which achieves fewer parameter updates, but slightly less test set accuracy as mentioned in details in the experiments’ section. In summary, on ImageNet dataset, Inception-ResNet-V2 achieved 77% validation accuracy in under 2500 parameter updates, and ResNet-50 achieved 76.1% validation set accuracy on TPU in less than 30 minutes. One of the great findings of this paper is that literature parameters were used, and no hyper parameter tuning was needed.<br />
<br />
== CRITIQUE ==<br />
'''Pros:'''<br />
<br />
- The paper showed empirically that increasing batch size and decaying learning rate are equivalent.<br />
<br />
- Several experiments were performed on different optimizers such as SGD and Adam.<br />
<br />
- Had several comparisons with previous experimental setups.<br />
<br />
'''Cons:'''<br />
<br />
<br />
- All datasets used are image datasets. Other experiments should have been done on datasets from different domains to ensure generalization. <br />
<br />
- The number of parameter updates was used as a comparison criterion, but wall-clock times could have provided additional measurable judgment although they depend on the hardware used.<br />
<br />
- Special hardware is needed for large batch training, which is not always feasible. As batch-size increases, we generally need more RAM to train the same model. However, if learning rate is decreased, the RAM use remains constant. As a result, learning rate decay will allow us to train bigger models.<br />
<br />
- In section 5.2 (Increasing the Effective Learning rate), the authors did not test a range of learning rate values and used only (0.1 and 0.5). Additional results from varying the initial learning rate values from 0.1 to 3.2 are provided in the appendix, which indicates that the test accuracy begins to fall for initial learning rates greater than ~0.4. The appended results do not show validation set accuracy curves like in Figure 6, however. It would be beneficial to see if they were similar to the original 0.1 and 0.5 initial learning rate baselines.<br />
<br />
- Although the main idea of the paper is interesting, its results does not seem to be too surprising in comparison with other recent papers in the subject.<br />
<br />
- The paper could benefit from using some other models to demonstrate its claim and generalize its idea by adding some comparisons with other models as well as other recent methods to increase batch size.<br />
<br />
- The paper presents interesting ideas. However, it lacks of mathematical and theoretical analysis beyond the idea. Since the experiment is primary on image dataset and it does not provide sufficient theories, the paper itself presents limited applicability to other types. <br />
<br />
- Also, in experimental setting, only single training runs from one random initialization is used. It would be better to take the best of many runs or to show confidence intervals.<br />
<br />
- It is proposed that we should compare learning rate decay with batch-size increase under the setting that total budget / number of training samples is fixed.<br />
<br />
== REFERENCES ==<br />
- Takuya Akiba, Shuji Suzuki, and Keisuke Fukuda. Extremely large minibatch sgd: Training resnet-50 on imagenet in 15 minutes. arXiv preprint arXiv:1711.04325, 2017.<br />
<br />
- Lukas Balles, Javier Romero, and Philipp Hennig. Coupling adaptive batch sizes with learning rates.arXiv preprint arXiv:1612.05086, 2016.<br />
<br />
- L´eon Bottou, Frank E Curtis, and Jorge Nocedal. Optimization methods for large-scale machine learning.arXiv preprint arXiv:1606.04838, 2016.<br />
<br />
- Richard H Byrd, Gillian M Chin, Jorge Nocedal, and Yuchen Wu. Sample size selection in optimization methods for machine learning. Mathematical programming, 134(1):127–155, 2012.<br />
<br />
- Pratik Chaudhari, Anna Choromanska, Stefano Soatto, and Yann LeCun. Entropy-SGD: Biasing gradient descent into wide valleys. arXiv preprint arXiv:1611.01838, 2016.<br />
<br />
- Soham De, Abhay Yadav, David Jacobs, and Tom Goldstein. Automated inference with adaptive batches. In Artificial Intelligence and Statistics, pp. 1504–1513, 2017.<br />
<br />
- Jeffrey Dean, Greg Corrado, Rajat Monga, Kai Chen, Matthieu Devin, Mark Mao, Andrew Senior, Paul Tucker, Ke Yang, Quoc V Le, et al. Large scale distributed deep networks. In Advances in neural information processing systems, pp. 1223–1231, 2012.<br />
<br />
- Michael P Friedlander and Mark Schmidt. Hybrid deterministic-stochastic methods for data fitting.SIAM Journal on Scientific Computing, 34(3):A1380–A1405, 2012.<br />
<br />
- Priya Goyal, Piotr Doll´ar, Ross Girshick, Pieter Noordhuis, Lukasz Wesolowski, Aapo Kyrola, Andrew Tulloch, Yangqing Jia, and Kaiming He. Accurate, large minibatch SGD: Training imagenet in 1 hour. arXiv preprint arXiv:1706.02677, 2017.<br />
<br />
- Sepp Hochreiter and J¨urgen Schmidhuber. Flat minima. Neural Computation, 9(1):1–42, 1997.<br />
<br />
- Elad Hoffer, Itay Hubara, and Daniel Soudry. Train longer, generalize better: closing the generalization gap in large batch training of neural networks. arXiv preprint arXiv:1705.08741, 2017.<br />
<br />
- Norman P Jouppi, Cliff Young, Nishant Patil, David Patterson, Gaurav Agrawal, Raminder Bajwa, Sarah Bates, Suresh Bhatia, Nan Boden, Al Borchers, et al. In-datacenter performance analysis of a tensor processing unit. In Proceedings of the 44th Annual International Symposium on Computer Architecture, pp. 1–12. ACM, 2017.<br />
<br />
- Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang. On large-batch training for deep learning: Generalization gap and sharp minima. arXiv preprint arXiv:1609.04836, 2016.<br />
<br />
- Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.<br />
<br />
- Alex Krizhevsky. One weird trick for parallelizing convolutional neural networks. arXiv preprint arXiv:1404.5997, 2014.<br />
<br />
- Qianxiao Li, Cheng Tai, and E Weinan. Stochastic modified equations and adaptive stochastic gradient algorithms. arXiv preprint arXiv:1511.06251, 2017.<br />
<br />
- Ilya Loshchilov and Frank Hutter. SGDR: stochastic gradient descent with restarts. arXiv preprint arXiv:1608.03983, 2016.<br />
<br />
- Stephan Mandt, Matthew D Hoffman, and DavidMBlei. Stochastic gradient descent as approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.<br />
<br />
- James Martens and Roger Grosse. Optimizing neural networks with kronecker-factored approximate curvature. In International Conference on Machine Learning, pp. 2408–2417, 2015.<br />
<br />
- Yurii Nesterov. A method of solving a convex programming problem with convergence rate o (1/k2). In Soviet Mathematics Doklady, volume 27, pp. 372–376, 1983.<br />
<br />
- Lutz Prechelt. Early stopping-but when? Neural Networks: Tricks of the trade, pp. 553–553, 1998.<br />
<br />
- Benjamin Recht, Christopher Re, Stephen Wright, and Feng Niu. Hogwild: A lock-free approach to parallelizing stochastic gradient descent. In Advances in neural information processing systems, pp. 693–701, 2011.<br />
<br />
- Herbert Robbins and Sutton Monro. A stochastic approximation method. The annals of mathematical statistics, pp. 400–407, 1951.<br />
<br />
- Samuel L. Smith and Quoc V. Le. A bayesian perspective on generalization and stochastic gradient descent. arXiv preprint arXiv:1710.06451, 2017.<br />
<br />
- Christian Szegedy, Sergey Ioffe, Vincent Vanhoucke, and Alexander A Alemi. Inception-v4, Inception-ResNet and the impact of residual connections on learning. In AAAI, pp. 4278–4284, 2017.<br />
<br />
- Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics. In Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 681–688, 2011.<br />
<br />
- Ashia C Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht. The marginal value of adaptive gradient methods in machine learning. arXiv preprint arXiv:1705.08292, 2017.<br />
<br />
- Yang You, Igor Gitman, and Boris Ginsburg. Scaling SGD batch size to 32k for imagenet training. arXiv preprint arXiv:1708.03888, 2017a.<br />
<br />
- Yang You, Zhao Zhang, C Hsieh, James Demmel, and Kurt Keutzer. Imagenet training in minutes. CoRR, abs/1709.05011, 2017b.<br />
<br />
- Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. arXiv preprint arXiv:1605.07146, 2016.<br />
<br />
- Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.</div>A22ravihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DON%27T_DECAY_THE_LEARNING_RATE_,_INCREASE_THE_BATCH_SIZE&diff=42029DON'T DECAY THE LEARNING RATE , INCREASE THE BATCH SIZE2018-11-30T10:54:19Z<p>A22ravi: /* STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION */</p>
<hr />
<div>Summary of the ICLR 2018 paper: '''Don't Decay the learning Rate, Increase the Batch Size ''' <br />
<br />
Link: [https://arxiv.org/pdf/1711.00489.pdf]<br />
<br />
Summarized by: Afify, Ahmed [ID: 20700841]<br />
<br />
==INTUITION==<br />
Nowadays, it is a common practice not to have a singular steady learning rate for the learning phase of neural network models. Instead, we use adaptive learning rates with the standard gradient descent method. The intuition behind this is that when we are far away from the minima, it is beneficial for us to take large steps towards the minima, as it would require a lesser number of steps to converge, but as we approach the minima, our step size should decrease, otherwise we may just keep oscillating around the minima. In practice, this is generally achieved by methods like SGD with momentum, Nesterov momentum, and Adam. However, the core claim of this paper is that the same effect can be achieved by increasing the batch size during the gradient descent process while keeping the learning rate constant throughout. In addition, the paper argues that such an approach also reduces the parameter updates required to reach the minima, thus leading to greater parallelism and shorter training times.<br />
<br />
== INTRODUCTION ==<br />
Stochastic gradient descent (SGD) is the most widely used optimization technique for training deep learning models. The reason for this is that the minima found using this process generalizes well (Zhang et al., 2016; Wilson et al., 2017), but the optimization process is slow and time consuming. According to (Goyal et al., 2017; Hoffer et al., 2017; You et al., 2017a), this has motivated researchers to try to speed up this optimization process by taking bigger steps, and hence reduce the number of parameter updates in training a model. This can be achieved by using large batch training, which can be divided across many machines. <br />
<br />
However, increasing the batch size leads to decreasing the test set accuracy (Keskar et al., 2016; Goyal et al., 2017). Smith and Le (2017) believed that SGD has a scale of random fluctuations <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N number of training samples, and B batch size. They concluded that there is an optimal batch size proportional to the learning rate when <math> B \ll N </math>, and optimum fluctuation scale <math>g</math> for a maximum test set accuracy.<br />
<br />
In this paper, the authors' main goal is to provide evidence that increasing the batch size is quantitatively equivalent to decreasing the learning rate with the same number of training epochs in decreasing the scale of random fluctuations, but with remarkably less number of parameter updates. Moreover, an additional reduction in the number of parameter updates can be attained by increasing the learning rate and scaling <math> B \propto \epsilon </math> or even more reduction by increasing the momentum coefficient and scaling <math> B \propto \frac{1}{1-m} </math> although the latter decreases the test accuracy. This has been demonstrated by several experiments on the ImageNet and CIFAR-10 datasets using ResNet-50 and Inception-ResNet-V2 architectures respectively.<br />
<br />
== STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION ==<br />
As mentioned in the previous section, the drawback of SGD when compared to full-batch training is the noise that it introduces that hinders optimization. According to (Robbins & Monro, 1951), there are two equations that govern how to reach the minimum of a convex function: (<math> \epsilon_i </math> denotes the learning rate at the <math> i^{th} </math> gradient update)<br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon_i = \infty </math>. This equation guarantees that we will reach the minimum. <br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon^2_i < \infty </math>. This equation, which is valid only for a fixed batch size, guarantees that learning rate decays fast enough allowing us to reach the minimum rather than bouncing due to noise.<br />
<br />
These equations indicate that the learning rate must decay during training, and second equation is only available when the batch size is constant. To change the batch size, Smith and Le (2017) proposed to interpret SGD as integrating this stochastic differential equation <math> \frac{dw}{dt} = -\frac{dC}{dw} + \eta(t) </math>, where C represents cost function, w represents the parameters, and η represents the Gaussian random noise. Furthermore, they proved that noise scale g controls the magnitude of random fluctuations in the training dynamics by this formula: <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N is the training set size and <math>B</math> is the batch size. As we usually have <math> B \ll N </math>, we can define <math> g \approx \epsilon \frac{N}{B} </math>. This explains why when the learning rate decreases, noise <math>g</math> decreases, enabling us to converge to the minimum of the cost function. However, increasing the batch size has the same effect and makes <math>g</math> decays with constant learning rate. In this work, the batch size is increased until <math> B \approx \frac{N}{10} </math>, then the conventional way of decaying the learning rate is followed.<br />
<br />
== SIMULATED ANNEALING AND THE GENERALIZATION GAP ==<br />
'''Simulated Annealing:''' decaying learning rates are empirically successful. To understand this, they note that introducing random fluctuations<br />
whose scale falls during training is also a well established technique in non-convex optimization; simulated annealing. The initial noisy optimization phase allows to explore a larger fraction of the parameter space without becoming trapped in local minima. Once a promising region of parameter space is located, the noise is reduced to fine-tune the parameters.<br />
<br />
For more info: Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as gradient descent. [https://en.wikipedia.org/wiki/Simulated_annealing [Reference]]<br />
<br />
'''Generalization Gap:''' Small batch data generalizes better to the test set than large batch data.<br />
<br />
Smith and Le (2017) found that there is an optimal batch size which corresponds to optimal noise scale g <math> (g \approx \epsilon \frac{N}{B}) </math> and concluded that <math> B_{opt} \propto \epsilon N </math> that corresponds to maximum test set accuracy. This means that gradient noise is helpful as it makes SGD escape sharp minima, which does not generalize well. <br />
<br />
Simulated Annealing is a famous technique in non-convex optimization. Starting with noise in the training process helps us to discover a wide range of parameters then once we are near the optimum value, noise is reduced to fine tune our final parameters. However, more and more researches like to use the sharper decay schedules like cosine decay or step-function drops. In physical sciences, slowly annealing (or decaying) the temperature (which is the noise scale in this situation) helps to converge to the global minimum, which is sharp. But decaying the temperature in discrete steps can make the system stuck in a local minimum, which lead to higher cost and lower curvature. The authors think that deep learning has the same intuition.<br />
.<br />
<br />
== THE EFFECTIVE LEARNING RATE AND THE ACCUMULATION VARIABLE ==<br />
'''The Effective Learning Rate''' : <math> \epsilon_{eff} = \frac{\epsilon}{1-m} </math><br />
<br />
Smith and Le (2017) included momentum to the equation of the vanilla SGD noise scale that was defined above to be: <math> g = \frac{\epsilon}{1-m}(\frac{N}{B}-1)\approx \frac{\epsilon N}{B(1-m)} </math>, which is the same as the previous equation when m goes to 0. They found that increasing the learning rate and momentum coefficient and scaling <math> B \propto \frac{\epsilon }{1-m} </math> reduces the number of parameter updates, but the test accuracy decreases when the momentum coefficient is increased. <br />
<br />
To understand the reasons behind this, we need to analyze momentum update equations below:<br />
<br />
<center><math><br />
\Delta A = -(1-m)A + \frac{d\widehat{C}}{dw} <br />
</math><br />
<br />
<math><br />
\Delta w = -A\epsilon<br />
</math><br />
</center><br />
<br />
We can see that the Accumulation variable A, which is initially set to 0, then increases exponentially to reach its steady state value during <math> \frac{B}{N(1-m)} </math> training epochs while <math> \Delta w </math> is suppressed that can reduce the rate of convergence. Moreover, at high momentum, we have three challenges:<br />
<br />
1- Additional epochs are needed to catch up with the accumulation.<br />
<br />
2- Accumulation needs more time <math> \frac{B}{N(1-m)} </math> to forget old gradients. <br />
<br />
3- After this time, however, the accumulation cannot adapt to changes in the loss landscape.<br />
<br />
4- In the early stage, large batch size will lead to the instabilities.<br />
<br />
== EXPERIMENTS ==<br />
=== SIMULATED ANNEALING IN A WIDE RESNET ===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Schedules used as in the below figure:''' <br />
<br />
- Decaying learning rate: learning rate decays by a factor of 5 at a sequence of “steps”, and the batch size is constant<br />
<br />
- Increasing batch size: learning rate is constant, and the batch size is increased by a factor of 5 at every step.<br />
<br />
- Hybrid: At the beginning, the learning rate is constant and batch size is increased by a factor of 5. Then, the learning rate decays by a factor of 5 at each subsequent step, and the batch size is constant. This is the schedule that will be used if there is a hardware limit affecting a maximum batch size limit.<br />
<br />
[[File:Paper_40_Fig_1.png